. . . . "2021-08-30"^^ . . . . . . . . "\u0413\u0438\u043F\u043E\u0301\u0442\u0435\u0437\u0430 \u041A\u043E\u0301\u043B\u043B\u0430\u0442\u0446\u0430 (3n+1 \u0434\u0438\u043B\u0435\u0301\u043C\u043C\u0430, \u0441\u0438\u0440\u0430\u043A\u0443\u0301\u0437\u0441\u043A\u0430\u044F \u043F\u0440\u043E\u0431\u043B\u0435\u0301\u043C\u0430) \u2014 \u043E\u0434\u043D\u0430 \u0438\u0437 \u043D\u0435\u0440\u0435\u0448\u0451\u043D\u043D\u044B\u0445 \u043F\u0440\u043E\u0431\u043B\u0435\u043C \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438.\u041F\u043E\u043B\u0443\u0447\u0438\u043B\u0430 \u0448\u0438\u0440\u043E\u043A\u0443\u044E \u0438\u0437\u0432\u0435\u0441\u0442\u043D\u043E\u0441\u0442\u044C \u0431\u043B\u0430\u0433\u043E\u0434\u0430\u0440\u044F \u043F\u0440\u043E\u0441\u0442\u043E\u0442\u0435 \u0444\u043E\u0440\u043C\u0443\u043B\u0438\u0440\u043E\u0432\u043A\u0438.\u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u043F\u043E \u0438\u043C\u0435\u043D\u0438 \u043D\u0435\u043C\u0435\u0446\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u041B\u043E\u0442\u0430\u0440\u0430 \u041A\u043E\u043B\u043B\u0430\u0442\u0446\u0430, \u0441\u0444\u043E\u0440\u043C\u0443\u043B\u0438\u0440\u043E\u0432\u0430\u0432\u0448\u0435\u0433\u043E \u044D\u0442\u0443 \u0437\u0430\u0434\u0430\u0447\u0443 1 \u0438\u044E\u043B\u044F 1932 \u0433\u043E\u0434\u0430."@ru . . . "\u0413\u0456\u043F\u043E\u0442\u0435\u0437\u0430 \u041A\u043E\u043B\u043B\u0430\u0442\u0446\u0430 (\u0433\u0456\u043F\u043E\u0442\u0435\u0437\u0430 3n+1, \u0433\u0456\u043F\u043E\u0442\u0435\u0437\u0430 3x+1, \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 \u041A\u043E\u043B\u043B\u0430\u0442\u0446\u0430, \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 3n+1, \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 3x+1, \u0421\u0456\u0440\u0430\u043A\u0443\u0437\u044C\u043A\u0430 \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430) \u2014 \u043E\u0434\u043D\u0430 \u0437 \u043D\u0435\u0440\u043E\u0437\u0432'\u044F\u0437\u0430\u043D\u0438\u0445 \u043F\u0440\u043E\u0431\u043B\u0435\u043C \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438, \u043D\u0430\u0437\u0432\u0430\u043D\u0430 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u043D\u0456\u043C\u0435\u0446\u044C\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u041B\u043E\u0442\u0430\u0440\u0430 \u041A\u043E\u043B\u043B\u0430\u0442\u0446\u0430, \u044F\u043A\u0438\u0439 \u0437\u0430\u043F\u0440\u043E\u043F\u043E\u043D\u0443\u0432\u0430\u0432 \u0457\u0457 \u0443 1937 \u0440\u043E\u0446\u0456."@uk . "\u8003\u62C9\u5179\u731C\u60F3\uFF08\u82F1\u8A9E\uFF1ACollatz conjecture\uFF09\uFF0C\u53C8\u79F0\u4E3A\u5947\u5076\u5F52\u4E00\u731C\u60F3\u30013n+1\u731C\u60F3\u3001\u51B0\u96F9\u731C\u60F3\u3001\u89D2\u8C37\u731C\u60F3\u3001\u54C8\u585E\u731C\u60F3\u3001\u4E4C\u62C9\u59C6\u731C\u60F3\u6216\u53D9\u62C9\u53E4\u731C\u60F3\uFF0C\u662F\u6307\u5BF9\u4E8E\u6BCF\u4E00\u4E2A\u6B63\u6574\u6570\uFF0C\u5982\u679C\u5B83\u662F\u5947\u6570\uFF0C\u5219\u5BF9\u5B83\u4E583\u518D\u52A01\uFF0C\u5982\u679C\u5B83\u662F\u5076\u6570\uFF0C\u5219\u5BF9\u5B83\u9664\u4EE52\uFF0C\u5982\u6B64\u5FAA\u73AF\uFF0C\u6700\u7EC8\u90FD\u80FD\u591F\u5F97\u52301\u3002"@zh . . . . . . . . . . "\u062D\u062F\u0633\u064A\u0629 \u0643\u0648\u0644\u0627\u062A\u0632"@ar . "La konjekto de Collatz (la konjekto de \u201C\u201D a\u016D la sirakuza problemo) estas unu el \u011Dis nun ne solvitaj matematikaj problemoj. La simpleco de \u011Dia formulado faris \u011Din vaste fama. La problemo estas nomata pro la nomo de la germana matematikisto , kiu formulis \u011Din en 1937."@eo . . . "\u30B3\u30E9\u30C3\u30C4\u306E\u554F\u984C"@ja . . . . "Collatz\u016Fv probl\u00E9m je v matematice domn\u011Bnka, kterou vyslovil Lothar Collatz. Tento probl\u00E9m je rovn\u011B\u017E zn\u00E1m\u00FD pod n\u00E1zvy 3n + 1 probl\u00E9m, Ulam\u016Fv probl\u00E9m (podle Stanis\u0142awa Ulama), Kakutan\u016Fv probl\u00E9m (podle \u0160izua Kakutaniho), Thwait\u016Fv probl\u00E9m (podle sira Bryana Thwaitese), Hass\u016Fv algoritmus (podle Helmuta Hasseho) nebo tak\u00E9 jako Syrakusk\u00FD probl\u00E9m. Posloupnost takto zkouman\u00FDch \u010D\u00EDsel se n\u011Bkdy naz\u00FDv\u00E1 t\u00E9\u017E jako posloupnost ledov\u00E9 kroupy (proto\u017Ee hodnota \u010D\u00EDsel v posloupnosti \u010Dasto mnohokr\u00E1t klesne a op\u011Bt se zv\u00FD\u0161\u00ED, podobn\u011B jako ledov\u00E9 kroupy m\u011Bn\u00ED svoji v\u00FD\u0161ku, kdy\u017E doch\u00E1z\u00ED k jejich tvorb\u011B v oblac\u00EDch)."@cs . . . . . "\u30B3\u30E9\u30C3\u30C4\u306E\u554F\u984C\uFF08\u30B3\u30E9\u30C3\u30C4\u306E\u3082\u3093\u3060\u3044\u3001Collatz problem\uFF09\u306F\u3001\u6570\u8AD6\u306E\u672A\u89E3\u6C7A\u554F\u984C\u306E\u3072\u3068\u3064\u3067\u3042\u308B\u3002\u554F\u984C\u306E\u7D50\u8AD6\u306E\u4E88\u60F3\u3092\u6307\u3057\u3066\u30B3\u30E9\u30C3\u30C4\u4E88\u60F3\u3068\u8A00\u3046\u3002\u4F1D\u7D71\u7684\u306B\u30ED\u30FC\u30BF\u30FC\u30FB\u30B3\u30E9\u30C3\u30C4\u306E\u540D\u3092\u51A0\u3055\u308C\u3066\u547C\u3070\u308C\u308B\u304C\u3001\u56FA\u6709\u540D\u8A5E\u306B\u4F9D\u62E0\u3057\u306A\u3044\u8868\u73FE\u3068\u3057\u3066\u306F3n+1\u554F\u984C\u3068\u3082\u8A00\u308F\u308C\u3001\u307E\u305F\u521D\u671F\u306B\u3053\u306E\u554F\u984C\u306B\u53D6\u308A\u7D44\u3093\u3060\u7814\u7A76\u8005\u306E\u540D\u3092\u51A0\u3057\u3066\u3001\u89D2\u8C37\u306E\u554F\u984C\u3001\u7C73\u7530\u306E\u4E88\u60F3\u3001\u30A6\u30E9\u30E0\u306E\u4E88\u60F3\u3001\u30B7\u30E9\u30AD\u30E5\u30FC\u30B9\u554F\u984C\u306A\u3069\u3068\u3082\u547C\u3070\u308C\u308B\u3002 \u6570\u5B66\u8005\u30DD\u30FC\u30EB\u30FB\u30A8\u30EB\u30C7\u30B7\u30E5\u306F\u300C\u6570\u5B66\u306F\u307E\u3060\u3053\u306E\u7A2E\u306E\u554F\u984C\u306B\u5BFE\u3059\u308B\u7528\u610F\u304C\u3067\u304D\u3066\u3044\u306A\u3044\u300D\u3068\u8FF0\u3079\u305F\u3002\u307E\u305F\u3001\u30B8\u30A7\u30D5\u30EA\u30FC\u30FB\u30E9\u30AC\u30EA\u30A2\u30B9\u306F2010\u5E74\u306B\u3001\u30B3\u30E9\u30C3\u30C4\u306E\u4E88\u60F3\u306F\u300C\u975E\u5E38\u306B\u96E3\u3057\u3044\u554F\u984C\u3067\u3042\u308A\u3001\u73FE\u4EE3\u306E\u6570\u5B66\u3067\u306F\u5B8C\u5168\u306B\u624B\u304C\u5C4A\u304B\u306A\u3044\u300D\u3068\u8FF0\u3079\u305F\u3002 2019\u5E7412\u6708\u3001\u30C6\u30EC\u30F3\u30B9\u30FB\u30BF\u30AA\u306F\u30B3\u30E9\u30C3\u30C4\u306E\u554F\u984C\u304C\u307B\u3068\u3093\u3069\u3059\u3079\u3066\u306E\u6B63\u306E\u6574\u6570\u306B\u304A\u3044\u3066\u307B\u3068\u3093\u3069\u6B63\u3057\u3044\u3068\u3059\u308B\u8AD6\u6587\u3092\u767A\u8868\u3057\u305F\u3002"@ja . "56082"^^ . . . . "A conjectura de Collatz \u00E9 uma conjectura matem\u00E1tica que recebeu este nome em refer\u00EAncia ao matem\u00E1tico alem\u00E3o Lothar Collatz, que foi o primeiro a prop\u00F4-la, em 1937. Al\u00E9m desse nome, este problema tamb\u00E9m \u00E9 conhecido por Problema 3x + 1, Conjectura de Ulam (pelo matem\u00E1tico polon\u00EAs-americano Stanis\u0142aw Marcin Ulam), Problema de Kakutani (pelo matem\u00E1tico nipo-americano Shizuo Kakutani), Conjectura de Thwaites (pelo acad\u00EAmico brit\u00E2nico ), Algoritmo de Hasse (pelo matem\u00E1tico alem\u00E3o Helmut Hasse) ou Problema de Siracusa. Esta conjectura aplica-se a qualquer n\u00FAmero natural inteiro, e diz-nos para, se este n\u00FAmero for par, o dividir por 2 (/2), e se for impar, para multiplicar por 3 e adicionar 1 (*3+1). Desta forma, por exemplo, se a sequ\u00EAncia iniciar com o n\u00FAmero 5 ter-se-\u00E1: 5; 16; 8; 4; 2; 1. A conjectura apresenta uma regra dizendo que, qualquer n\u00FAmero natural inteiro, quando aplicado a esta regra, eventualmente sempre chegar\u00E1 a 4, que se converte em 2 e termina em 1. Essa sequ\u00EAncia em quest\u00E3o tamb\u00E9m pode ser chamada de N\u00FAmeros de Granizo ou N\u00FAmeros Maravilhosos. A explica\u00E7\u00E3o destes \u00FAltimos nomes est\u00E1 em \"como o granizo nas nuvens antes de cair, os n\u00FAmeros saltam de um lugar ao outro antes de chegar ao 4, 2, 1\". A explica\u00E7\u00E3o para estes saltos, quando ocorrem N\u00FAmeros de Granizo, est\u00E1 na quantidade de fatores primos iguais a 2 quando decompomos este n\u00FAmero, o que determina quantas vezes, de forma sucessiva, ser\u00E1 aplicada a conjectura para n\u00FAmeros pares f(x)=x/2. Por exemplo, a en\u00E9sima pot\u00EAncia de 2 (2n) chegar\u00E1 a 1 em n passos, o que demonstra ser infinita a abrang\u00EAncia da Conjectura de Collatz. O matem\u00E1tico alem\u00E3o Gerhard Opfer publicou em maio de 2011 um artigo com o teorema que supostamente provava esta conjectura, causando alvoro\u00E7o na comunidade matem\u00E1tica.. Em 17 de julho de 2011, entretanto, o autor publicou uma nota, na \u00FAltima p\u00E1gina de seu artigo, onde reconhecia que uma de suas afirma\u00E7\u00F5es estava incompleta, o que n\u00E3o garantia a ele a prova do problema. A Tabela a seguir descreve a porcentagem de n\u00FAmeros pares e \u00EDmpares para a quantidade de n\u00FAmeros dados. Em geral, ocorre o dobro de n\u00FAmeros pares em rela\u00E7\u00E3o aos \u00EDmpares conforme mostrado nessa tabela."@pt . "Conjectura de Collatz"@pt . . . "The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns sequences of integers in which each term is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that these sequences always reach 1, no matter which positive integer is chosen to start the sequence. It is named after mathematician Lothar Collatz, who introduced the idea in 1937, two years after receiving his doctorate. It is also known as the 3n + 1 problem, the 3n + 1 conjecture, the Ulam conjecture (after Stanis\u0142aw Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem. The sequence of numbers involved is sometimes referred to as the hailstone sequence, hailstone numbers or hailstone numerals (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers. Paul Erd\u0151s said about the Collatz conjecture: \"Mathematics may not be ready for such problems.\" He also offered US$500 for its solution. Jeffrey Lagarias stated in 2010 that the Collatz conjecture \"is an extraordinarily difficult problem, completely out of reach of present day mathematics\"."@en . . . "Collatzen aierua matematikako aieru bat da, honela definitutako sekuentziei dagokiena: hasi edozein zenbaki oso positiborekin n. Beraz, termino bakoitza honela ateratzen da aurreko terminotik: aurreko terminoa bikoitia bada, hurrengo terminoa aurreko terminoaren erdia da. Aurreko terminoa bakoitia bada, hurrengo terminoa aurreko terminoa bider 3 gehi 1 da. Ustea zera da, n-ren balioa zeinahi dela ere, sekuentzia beti iritsiko da 1 zenbakira. matematikariarengandik hartu du izena aieruak, 1937an sartu baitzuen ideia, doktoretza jaso eta bi urtera. Izen hauek ere hartzen ditu aieruak: 3n + 1 arazoa, 3n + 1 aierua, Ulamen aierua (Stanis\u0627aw Ulamen arabera), Kakutaniren arazoa (Shizuo Kakutaniren arabera), Thwaitesen aierua (Sir Bryan Thwaitesen arabera), Hasseren algoritmoa (Helmut Hasseren arabera), edo Sirakusako arazoa. Parte hartzen duten zenbakien sekuentziari, batzuetan, kazkabar-sekuentzia edo txingor-zenbakiak esaten zaio (izan ere, balioek, oro har, jaitsiera eta igoera ugari izaten dituzte, hala nola hodei bateko txingorra), edo zenbaki zoragarriak."@eu . "CollatzProblem"@en . "La congettura di Collatz (conosciuta anche come congettura 3n + 1, congettura di Syracuse, congettura di Ulam o numeri di Hailstone) \u00E8 una congettura matematica tuttora irrisolta. Fu enunciata per la prima volta nel 1937 da Lothar Collatz, da cui prende il nome. Paul Erd\u0151s disse, circa questa congettura, che \u00ABla matematica non \u00E8 ancora matura per problemi di questo tipo\u00BB, e offr\u00EC 500 dollari per la sua soluzione."@it . "Het vermoeden van Collatz is een vermoeden in de getaltheorie dat zegt dat een bepaalde iteratie in alle gevallen uitloopt op het getal 1, om het even welk getal als beginwaarde gekozen wordt."@nl . . "Problem Collatza (znany te\u017C jako problem 3x+1, problem Ulama, problem Kakutaniego, problem syrakuza\u0144ski) \u2013 nierozstrzygni\u0119ty dotychczas problem o wyj\u0105tkowo prostym \u2013 jak wiele innych problem\u00F3w teorii liczb \u2013 sformu\u0142owaniu. Nazwa pochodzi od nazwiska niemieckiego matematyka Lothara Collatza (1937). Zagadnienie to by\u0142o r\u00F3wnie\u017C rozpatrywane przez polskiego matematyka Stanis\u0142awa Ulama, a tak\u017Ce przez ."@pl . . "Collatzen aierua matematikako aieru bat da, honela definitutako sekuentziei dagokiena: hasi edozein zenbaki oso positiborekin n. Beraz, termino bakoitza honela ateratzen da aurreko terminotik: aurreko terminoa bikoitia bada, hurrengo terminoa aurreko terminoaren erdia da. Aurreko terminoa bakoitia bada, hurrengo terminoa aurreko terminoa bider 3 gehi 1 da. Ustea zera da, n-ren balioa zeinahi dela ere, sekuentzia beti iritsiko da 1 zenbakira."@eu . "\u0395\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 \u03C4\u03BF\u03C5 \u039A\u03CC\u03BB\u03B1\u03C4\u03B6"@el . . . . . . . . "Congettura di Collatz"@it . . . "Conjectura de Collatz"@ca . . . . . . . "A conjectura de Collatz \u00E9 uma conjectura matem\u00E1tica que recebeu este nome em refer\u00EAncia ao matem\u00E1tico alem\u00E3o Lothar Collatz, que foi o primeiro a prop\u00F4-la, em 1937. Al\u00E9m desse nome, este problema tamb\u00E9m \u00E9 conhecido por Problema 3x + 1, Conjectura de Ulam (pelo matem\u00E1tico polon\u00EAs-americano Stanis\u0142aw Marcin Ulam), Problema de Kakutani (pelo matem\u00E1tico nipo-americano Shizuo Kakutani), Conjectura de Thwaites (pelo acad\u00EAmico brit\u00E2nico ), Algoritmo de Hasse (pelo matem\u00E1tico alem\u00E3o Helmut Hasse) ou Problema de Siracusa."@pt . . . . "Collatz\u016Fv probl\u00E9m je v matematice domn\u011Bnka, kterou vyslovil Lothar Collatz. Tento probl\u00E9m je rovn\u011B\u017E zn\u00E1m\u00FD pod n\u00E1zvy 3n + 1 probl\u00E9m, Ulam\u016Fv probl\u00E9m (podle Stanis\u0142awa Ulama), Kakutan\u016Fv probl\u00E9m (podle \u0160izua Kakutaniho), Thwait\u016Fv probl\u00E9m (podle sira Bryana Thwaitese), Hass\u016Fv algoritmus (podle Helmuta Hasseho) nebo tak\u00E9 jako Syrakusk\u00FD probl\u00E9m. Posloupnost takto zkouman\u00FDch \u010D\u00EDsel se n\u011Bkdy naz\u00FDv\u00E1 t\u00E9\u017E jako posloupnost ledov\u00E9 kroupy (proto\u017Ee hodnota \u010D\u00EDsel v posloupnosti \u010Dasto mnohokr\u00E1t klesne a op\u011Bt se zv\u00FD\u0161\u00ED, podobn\u011B jako ledov\u00E9 kroupy m\u011Bn\u00ED svoji v\u00FD\u0161ku, kdy\u017E doch\u00E1z\u00ED k jejich tvorb\u011B v oblac\u00EDch). Domn\u011Bnka m\u016F\u017Ee b\u00FDt shrnuta n\u00E1sledovn\u011B. Vezm\u011Bme jak\u00E9koliv kladn\u00E9 cel\u00E9 \u010D\u00EDslo n. Pokud je n sud\u00FDm \u010D\u00EDslem, vyd\u011Bl\u00EDme je dv\u011Bma, z\u00EDsk\u00E1me tak n / 2. Pokud je n lich\u00FDm \u010D\u00EDslem, vyn\u00E1sob\u00ED se t\u0159emi a p\u0159i\u010Dte se jedni\u010Dka, tj. 3n + 1. Tento postup (v angli\u010Dtin\u011B naz\u00FDvan\u00FD tak\u00E9 \u201EHalf Or Triple Plus One\u201C nebo HOTPO) se d\u00E1le opakuje. Domn\u011Bnka je takov\u00E1, \u017Ee nehled\u011B na to, jak\u00E9 po\u010D\u00E1te\u010Dn\u00ED \u010D\u00EDslo n je zvoleno \u2013 v\u00FDsledn\u00E1 posloupnost v\u017Edy nakonec dojde k \u010D\u00EDslu 1."@cs . . . . . . "La conjetura de Collatz, conocida tambi\u00E9n como conjetura 3n+1 o conjetura de Ulam (entre otros nombres), fue enunciada por el matem\u00E1tico Lothar Collatz en 1937, y a la fecha no se ha resuelto."@es . "\u0413\u0438\u043F\u043E\u0301\u0442\u0435\u0437\u0430 \u041A\u043E\u0301\u043B\u043B\u0430\u0442\u0446\u0430 (3n+1 \u0434\u0438\u043B\u0435\u0301\u043C\u043C\u0430, \u0441\u0438\u0440\u0430\u043A\u0443\u0301\u0437\u0441\u043A\u0430\u044F \u043F\u0440\u043E\u0431\u043B\u0435\u0301\u043C\u0430) \u2014 \u043E\u0434\u043D\u0430 \u0438\u0437 \u043D\u0435\u0440\u0435\u0448\u0451\u043D\u043D\u044B\u0445 \u043F\u0440\u043E\u0431\u043B\u0435\u043C \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438.\u041F\u043E\u043B\u0443\u0447\u0438\u043B\u0430 \u0448\u0438\u0440\u043E\u043A\u0443\u044E \u0438\u0437\u0432\u0435\u0441\u0442\u043D\u043E\u0441\u0442\u044C \u0431\u043B\u0430\u0433\u043E\u0434\u0430\u0440\u044F \u043F\u0440\u043E\u0441\u0442\u043E\u0442\u0435 \u0444\u043E\u0440\u043C\u0443\u043B\u0438\u0440\u043E\u0432\u043A\u0438.\u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u043F\u043E \u0438\u043C\u0435\u043D\u0438 \u043D\u0435\u043C\u0435\u0446\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u041B\u043E\u0442\u0430\u0440\u0430 \u041A\u043E\u043B\u043B\u0430\u0442\u0446\u0430, \u0441\u0444\u043E\u0440\u043C\u0443\u043B\u0438\u0440\u043E\u0432\u0430\u0432\u0448\u0435\u0433\u043E \u044D\u0442\u0443 \u0437\u0430\u0434\u0430\u0447\u0443 1 \u0438\u044E\u043B\u044F 1932 \u0433\u043E\u0434\u0430."@ru . . "\uCF5C\uB77C\uCE20 \uCD94\uCE21"@ko . "Conjecture de Syracuse"@fr . "Het vermoeden van Collatz is een vermoeden in de getaltheorie dat zegt dat een bepaalde iteratie in alle gevallen uitloopt op het getal 1, om het even welk getal als beginwaarde gekozen wordt."@nl . . . . "Collatz conjecture"@en . . . . . "The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns sequences of integers in which each term is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that these sequences always reach 1, no matter which positive integer is chosen to start the sequence."@en . . . . . . . . "Collatz\u016Fv probl\u00E9m"@cs . . . . . . "\u8003\u62C9\u5179\u731C\u60F3"@zh . "\uCF5C\uB77C\uCE20 \uCD94\uCE21(Collatz conjecture)\uC740 1937\uB144\uC5D0 \uCC98\uC74C\uC73C\uB85C \uC774 \uCD94\uCE21\uC744 \uC81C\uAE30\uD55C \uB85C\uD0C0\uB974 \uCF5C\uB77C\uCE20\uC758 \uC774\uB984\uC744 \uB534 \uAC83\uC73C\uB85C 3n+1 \uCD94\uCE21, \uC6B8\uB78C \uCD94\uCE21, \uD639\uC740 \uD5E4\uC77C\uC2A4\uD1A4(\uC6B0\uBC15) \uC218\uC5F4 \uB4F1 \uC5EC\uB7EC \uC774\uB984\uC73C\uB85C \uBD88\uB9B0\uB2E4. \uCF5C\uB77C\uCE20 \uCD94\uCE21\uC740 \uC784\uC758\uC758 \uC790\uC5F0\uC218\uAC00 \uB2E4\uC74C \uC870\uC791\uC744 \uAC70\uCCD0 \uD56D\uC0C1 1\uC774 \uB41C\uB2E4\uB294 \uCD94\uCE21\uC774\uB2E4. 1. \n* \uC9DD\uC218\uB77C\uBA74 2\uB85C \uB098\uB208\uB2E4. 2. \n* \uD640\uC218\uB77C\uBA74 3\uC744 \uACF1\uD558\uACE0 1\uC744 \uB354\uD55C\uB2E4. 3. \n* 1\uC774\uBA74 \uC870\uC791\uC744 \uBA48\uCD94\uACE0, 1\uC774 \uC544\uB2C8\uBA74 \uCCAB \uBC88\uC9F8 \uB2E8\uACC4\uB85C \uB3CC\uC544\uAC04\uB2E4. \uC608\uB97C \uB4E4\uC5B4, 6\uC5D0\uC11C \uC2DC\uC791\uD55C\uB2E4\uBA74, \uCC28\uB840\uB85C 6, 3, 10, 5, 16, 8, 4, 2, 1 \uC774 \uB41C\uB2E4. \uB610, 27\uC5D0\uC11C \uC2DC\uC791\uD558\uBA74 \uBB34\uB824 111\uBC88\uC744 \uAC70\uCCD0\uC57C 1\uC774 \uB41C\uB2E4. 77\uBC88\uC9F8\uC5D0 \uC774\uB974\uBA74 9232\uB97C \uC815\uC810\uC73C\uB85C \uB3C4\uB2EC\uD558\uB2E4\uAC00 \uAE09\uACA9\uD788 \uAC10\uC18C\uD558\uC5EC 34\uB2E8\uACC4\uB97C \uB354 \uC9C0\uB098\uBA74 1\uC774 \uB41C\uB2E4. \uC774 \uCD94\uCE21\uC740 \uCEF4\uD4E8\uD130\uB85C 268\uAE4C\uC9C0 \uBAA8\uB450 \uC131\uB9BD\uD568\uC774 \uD655\uC778\uB418\uC5C8\uB2E4. \uADF8\uB7EC\uB098, \uC544\uC9C1 \uBAA8\uB4E0 \uC790\uC5F0\uC218\uC5D0 \uB300\uD55C \uC99D\uBA85\uC740 \uBC1C\uACAC\uB418\uC9C0 \uC54A\uACE0 \uC788\uB2E4. \uC774 \uBB38\uC81C\uC758 \uD574\uACB0\uC5D0 500\uB2EC\uB7EC\uC758 \uD604\uC0C1\uAE08\uC744 \uAC78\uC5C8\uB358 \uC5D0\uB974\uB418\uC2DC \uD314\uC740 \"\uC218\uD559\uC740 \uC544\uC9C1 \uC774\uB7F0 \uBB38\uC81C\uB97C \uB2E4\uB8F0 \uC900\uBE44\uAC00 \uB418\uC5B4 \uC788\uC9C0 \uC54A\uB2E4.\"\uB294 \uB9D0\uC744 \uB0A8\uACBC\uB2E4."@ko . . . . . "\u062D\u062F\u0633\u064A\u0629 \u0643\u0648\u0644\u0627\u062A\u0632 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Collatz conjecture)\u200F \u0647\u064A \u062D\u062F\u0633\u064A\u0629 \u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0633\u0645\u064A\u062A \u0647\u0643\u0630\u0627 \u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0644\u0648\u062B\u0627\u0631 \u0643\u0648\u0644\u0627\u062A\u0632, \u062D\u062F\u0633\u0647\u0627 \u0639\u0627\u0645 1937. \u0642\u062F \u062A\u0633\u0645\u0649 \u0623\u064A\u0636\u0627 \u062D\u062F\u0633\u064A\u0629 3n + 1 \u0648 \u062D\u062F\u0633\u064A\u0629 \u0623\u0648\u0644\u0627\u0645 (\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0627\u0644\u0639\u0627\u0644\u0645 \u0627\u0644\u0628\u0648\u0644\u0646\u062F\u064A \u0633\u062A\u0627\u0646\u064A\u0633\u0644\u0648 \u0623\u0648\u0644\u0627\u0645) \u0648 \u0645\u0639\u0636\u0644\u0629 \u0643\u0627\u0643\u0648\u062A\u0627\u0646\u064A (\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 ) \u0648 \u062D\u062F\u0633\u064A\u0629 \u062A\u0648\u0627\u064A\u062A\u0633 (\u0646\u0633\u0628\u0629 \u0625\u0644\u064A ) \u0648\u062E\u0648\u0627\u0631\u0632\u0645\u064A\u0629 \u0647\u0627\u0633 (\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0647\u064A\u0644\u0645\u0648\u062A \u0647\u0627\u0633) \u0648\u0645\u0639\u0636\u0644\u0629 \u0633\u064A\u0631\u0627\u0643\u0648\u0632. \u0642\u0627\u0644 \u0628\u0648\u0644 \u0625\u064A\u0631\u062F\u0648\u0633 \u0639\u0646 \u0647\u0630\u0647 \u0627\u0644\u062D\u062F\u0633\u064A\u0629 : \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0644\u064A\u0633\u062A \u0646\u0627\u0636\u062C\u0629 \u0628\u0645\u0627 \u0641\u064A\u0647 \u0627\u0644\u0643\u0641\u0627\u064A\u0629 \u0644\u0643\u064A \u062A\u062D\u0644\u062D\u0644 \u0645\u0639\u0636\u0644\u0629 \u0643\u0647\u0630\u0647\u060C \u0643\u0645\u0627 \u0645\u0646\u062D \u062C\u0627\u0626\u0632\u0629 \u062E\u0645\u0633\u0645\u0627\u0626\u0629 \u062F\u0648\u0644\u0627\u0631 \u0623\u0645\u0631\u064A\u0643\u064A \u0644\u0645\u0646 \u064A\u062D\u0644\u062D\u0644\u0647\u0627. \u0641\u064A \u0639\u0627\u0645 2007\u060C \u0623\u064F\u062B\u0628\u062A \u0623\u0646 \u0623\u064A \u062A\u0639\u0645\u064A\u0645 \u0637\u0628\u064A\u0639\u064A \u0644\u0645\u0639\u0636\u0644\u0629 \u0643\u0648\u0644\u0627\u062A\u0632 \u0647\u0648 \u0645\u0639\u0636\u0644\u0629 \u063A\u064A\u0631 \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u0642\u0631\u0627\u0631 \u0645\u0646 \u0627\u0644\u0648\u062C\u0647\u0629 \u0627\u0644\u062E\u0648\u0627\u0631\u0632\u0645\u064A\u0629."@ar . "La conjecture de Syracuse, encore appel\u00E9e conjecture de Collatz, conjecture d'Ulam, conjecture tch\u00E8que ou probl\u00E8me 3x + 1, est l'hypoth\u00E8se math\u00E9matique selon laquelle la suite de Syracuse de n'importe quel entier strictement positif atteint 1. Une suite de Syracuse est une suite d'entiers naturels d\u00E9finie de la mani\u00E8re suivante : on part d'un nombre entier strictement positif ; s\u2019il est pair, on le divise par 2 ; s\u2019il est impair, on le multiplie par 3 et l'on ajoute 1. En r\u00E9p\u00E9tant l\u2019op\u00E9ration, on obtient une suite d'entiers strictement positifs dont chacun ne d\u00E9pend que de son pr\u00E9d\u00E9cesseur. Par exemple, \u00E0 partir de 14, on construit la suite des nombres : 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 4, 2\u2026 C'est la suite de Syracuse du nombre 14. Apr\u00E8s que le nombre 1 a \u00E9t\u00E9 atteint, la suite des valeurs 1, 4, 2, 1, 4, 2\u2026 se r\u00E9p\u00E8te ind\u00E9finiment en un cycle de longueur 3, appel\u00E9 cycle trivial. Si l'on \u00E9tait parti d'un autre entier, en lui appliquant les m\u00EAmes r\u00E8gles, on aurait obtenu une suite de nombres diff\u00E9rente. A priori, il serait possible que la suite de Syracuse de certaines valeurs de d\u00E9part n'atteigne jamais la valeur 1, soit qu'elle aboutisse \u00E0 un cycle diff\u00E9rent du cycle trivial, soit qu'elle diverge vers l'infini. Or, on n'a jamais trouv\u00E9 d'exemple de suite obtenue suivant les r\u00E8gles donn\u00E9es qui n'aboutisse pas \u00E0 1, puis au cycle trivial. En d\u00E9pit de la simplicit\u00E9 de son \u00E9nonc\u00E9, cette conjecture d\u00E9fie depuis de nombreuses ann\u00E9es les math\u00E9maticiens. Paul Erd\u0151s a dit \u00E0 propos de la conjecture de Syracuse : \u00AB les math\u00E9matiques ne sont pas encore pr\u00EAtes pour de tels probl\u00E8mes. \u00BB"@fr . . "Collatz problem \u00E4r ett ol\u00F6st problem inom talteorin. Problemet kallas \u00E4ven f\u00F6r bland annat Collatz f\u00F6rmodan, Ulam-f\u00F6rmodan och 3n+1-f\u00F6rmodan. formulerade problemet under sin tid som student. Problemet utg\u00E5r fr\u00E5n en r\u00E4knelek som b\u00F6rjar med ett positivt heltal n. N\u00E4sta steg \u00E4r att dela n med tv\u00E5 om det \u00E4r j\u00E4mnt, eller multiplicera det med tre och addera ett om det \u00E4r udda. Sedan upprepas detta steg med talet som erh\u00F6lls genom utr\u00E4kningen till dess att resultatet blir ett. Detta kan skrivas som en talf\u00F6ljd. Collatz problem \u00E4r att avg\u00F6ra om man, oavsett vilket tal man b\u00F6rjar med, kan n\u00E5 talet ett. Problemet \u00E4r ekvivalent med att avg\u00F6ra om det finns n\u00E5gon cykel av tal som inte inneh\u00E5ller ett och om det finns n\u00E5got tal som v\u00E4xer o\u00E4ndligt stort; om n\u00E5got av dessa tv\u00E5 saker existerar \u00E4r f\u00F6rmodand"@sv . . . "La conjectura de Collatz \u00E9s un dels problemes no resolts m\u00E9s famosos de les matem\u00E0tiques. La conjectura es pregunta si repetir dues operacions aritm\u00E8tiques simples acabar\u00E0 transformant cada nombre enter positiu en 1. La seq\u00FC\u00E8ncia de n\u00FAmeros implicada de vegades es coneix com a seq\u00FC\u00E8ncia de calamarsa, n\u00FAmeros de calamarsa o n\u00FAmerals de calamarsa (perqu\u00E8 els valors solen estar subjectes a m\u00FAltiples baixades i ascensos com la calamarsa en un n\u00FAvol), o com a nombres meravellosos."@ca . . . . . . . . . . "Problem Collatza"@pl . . . . . . . . "Collatz problem \u00E4r ett ol\u00F6st problem inom talteorin. Problemet kallas \u00E4ven f\u00F6r bland annat Collatz f\u00F6rmodan, Ulam-f\u00F6rmodan och 3n+1-f\u00F6rmodan. formulerade problemet under sin tid som student. Problemet utg\u00E5r fr\u00E5n en r\u00E4knelek som b\u00F6rjar med ett positivt heltal n. N\u00E4sta steg \u00E4r att dela n med tv\u00E5 om det \u00E4r j\u00E4mnt, eller multiplicera det med tre och addera ett om det \u00E4r udda. Sedan upprepas detta steg med talet som erh\u00F6lls genom utr\u00E4kningen till dess att resultatet blir ett. Detta kan skrivas som en talf\u00F6ljd. Collatz problem \u00E4r att avg\u00F6ra om man, oavsett vilket tal man b\u00F6rjar med, kan n\u00E5 talet ett. Problemet \u00E4r ekvivalent med att avg\u00F6ra om det finns n\u00E5gon cykel av tal som inte inneh\u00E5ller ett och om det finns n\u00E5got tal som v\u00E4xer o\u00E4ndligt stort; om n\u00E5got av dessa tv\u00E5 saker existerar \u00E4r f\u00F6rmodandet falsifierat, annars \u00E4r det sant. Dessutom g\u00E5r det att omformulera problemet ytterligare. Datorber\u00E4kningar anv\u00E4nds f\u00F6r att unders\u00F6ka och f\u00F6rs\u00F6ka hitta en l\u00F6sning till Collatz problem. \u00C4n s\u00E5 l\u00E4nge har ingen kunnat avg\u00F6ra huruvida alla talf\u00F6ljder slutar med ett, s\u00E5 problemet \u00E4r ol\u00F6st."@sv . . . "La konjekto de Collatz (la konjekto de \u201C\u201D a\u016D la sirakuza problemo) estas unu el \u011Dis nun ne solvitaj matematikaj problemoj. La simpleco de \u011Dia formulado faris \u011Din vaste fama. La problemo estas nomata pro la nomo de la germana matematikisto , kiu formulis \u011Din en 1937."@eo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "37895"^^ . "\u062D\u062F\u0633\u064A\u0629 \u0643\u0648\u0644\u0627\u062A\u0632 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Collatz conjecture)\u200F \u0647\u064A \u062D\u062F\u0633\u064A\u0629 \u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0633\u0645\u064A\u062A \u0647\u0643\u0630\u0627 \u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0644\u0648\u062B\u0627\u0631 \u0643\u0648\u0644\u0627\u062A\u0632, \u062D\u062F\u0633\u0647\u0627 \u0639\u0627\u0645 1937. \u0642\u062F \u062A\u0633\u0645\u0649 \u0623\u064A\u0636\u0627 \u062D\u062F\u0633\u064A\u0629 3n + 1 \u0648 \u062D\u062F\u0633\u064A\u0629 \u0623\u0648\u0644\u0627\u0645 (\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0627\u0644\u0639\u0627\u0644\u0645 \u0627\u0644\u0628\u0648\u0644\u0646\u062F\u064A \u0633\u062A\u0627\u0646\u064A\u0633\u0644\u0648 \u0623\u0648\u0644\u0627\u0645) \u0648 \u0645\u0639\u0636\u0644\u0629 \u0643\u0627\u0643\u0648\u062A\u0627\u0646\u064A (\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 ) \u0648 \u062D\u062F\u0633\u064A\u0629 \u062A\u0648\u0627\u064A\u062A\u0633 (\u0646\u0633\u0628\u0629 \u0625\u0644\u064A ) \u0648\u062E\u0648\u0627\u0631\u0632\u0645\u064A\u0629 \u0647\u0627\u0633 (\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0647\u064A\u0644\u0645\u0648\u062A \u0647\u0627\u0633) \u0648\u0645\u0639\u0636\u0644\u0629 \u0633\u064A\u0631\u0627\u0643\u0648\u0632. \u0642\u0627\u0644 \u0628\u0648\u0644 \u0625\u064A\u0631\u062F\u0648\u0633 \u0639\u0646 \u0647\u0630\u0647 \u0627\u0644\u062D\u062F\u0633\u064A\u0629 : \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0644\u064A\u0633\u062A \u0646\u0627\u0636\u062C\u0629 \u0628\u0645\u0627 \u0641\u064A\u0647 \u0627\u0644\u0643\u0641\u0627\u064A\u0629 \u0644\u0643\u064A \u062A\u062D\u0644\u062D\u0644 \u0645\u0639\u0636\u0644\u0629 \u0643\u0647\u0630\u0647\u060C \u0643\u0645\u0627 \u0645\u0646\u062D \u062C\u0627\u0626\u0632\u0629 \u062E\u0645\u0633\u0645\u0627\u0626\u0629 \u062F\u0648\u0644\u0627\u0631 \u0623\u0645\u0631\u064A\u0643\u064A \u0644\u0645\u0646 \u064A\u062D\u0644\u062D\u0644\u0647\u0627. \u0641\u064A \u0639\u0627\u0645 2007\u060C \u0623\u064F\u062B\u0628\u062A \u0623\u0646 \u0623\u064A \u062A\u0639\u0645\u064A\u0645 \u0637\u0628\u064A\u0639\u064A \u0644\u0645\u0639\u0636\u0644\u0629 \u0643\u0648\u0644\u0627\u062A\u0632 \u0647\u0648 \u0645\u0639\u0636\u0644\u0629 \u063A\u064A\u0631 \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u0642\u0631\u0627\u0631 \u0645\u0646 \u0627\u0644\u0648\u062C\u0647\u0629 \u0627\u0644\u062E\u0648\u0627\u0631\u0632\u0645\u064A\u0629."@ar . . . . . "Collatz-Problem"@de . . . "\uCF5C\uB77C\uCE20 \uCD94\uCE21(Collatz conjecture)\uC740 1937\uB144\uC5D0 \uCC98\uC74C\uC73C\uB85C \uC774 \uCD94\uCE21\uC744 \uC81C\uAE30\uD55C \uB85C\uD0C0\uB974 \uCF5C\uB77C\uCE20\uC758 \uC774\uB984\uC744 \uB534 \uAC83\uC73C\uB85C 3n+1 \uCD94\uCE21, \uC6B8\uB78C \uCD94\uCE21, \uD639\uC740 \uD5E4\uC77C\uC2A4\uD1A4(\uC6B0\uBC15) \uC218\uC5F4 \uB4F1 \uC5EC\uB7EC \uC774\uB984\uC73C\uB85C \uBD88\uB9B0\uB2E4. \uCF5C\uB77C\uCE20 \uCD94\uCE21\uC740 \uC784\uC758\uC758 \uC790\uC5F0\uC218\uAC00 \uB2E4\uC74C \uC870\uC791\uC744 \uAC70\uCCD0 \uD56D\uC0C1 1\uC774 \uB41C\uB2E4\uB294 \uCD94\uCE21\uC774\uB2E4. 1. \n* \uC9DD\uC218\uB77C\uBA74 2\uB85C \uB098\uB208\uB2E4. 2. \n* \uD640\uC218\uB77C\uBA74 3\uC744 \uACF1\uD558\uACE0 1\uC744 \uB354\uD55C\uB2E4. 3. \n* 1\uC774\uBA74 \uC870\uC791\uC744 \uBA48\uCD94\uACE0, 1\uC774 \uC544\uB2C8\uBA74 \uCCAB \uBC88\uC9F8 \uB2E8\uACC4\uB85C \uB3CC\uC544\uAC04\uB2E4. \uC608\uB97C \uB4E4\uC5B4, 6\uC5D0\uC11C \uC2DC\uC791\uD55C\uB2E4\uBA74, \uCC28\uB840\uB85C 6, 3, 10, 5, 16, 8, 4, 2, 1 \uC774 \uB41C\uB2E4. \uB610, 27\uC5D0\uC11C \uC2DC\uC791\uD558\uBA74 \uBB34\uB824 111\uBC88\uC744 \uAC70\uCCD0\uC57C 1\uC774 \uB41C\uB2E4. 77\uBC88\uC9F8\uC5D0 \uC774\uB974\uBA74 9232\uB97C \uC815\uC810\uC73C\uB85C \uB3C4\uB2EC\uD558\uB2E4\uAC00 \uAE09\uACA9\uD788 \uAC10\uC18C\uD558\uC5EC 34\uB2E8\uACC4\uB97C \uB354 \uC9C0\uB098\uBA74 1\uC774 \uB41C\uB2E4. \uC774 \uCD94\uCE21\uC740 \uCEF4\uD4E8\uD130\uB85C 268\uAE4C\uC9C0 \uBAA8\uB450 \uC131\uB9BD\uD568\uC774 \uD655\uC778\uB418\uC5C8\uB2E4. \uADF8\uB7EC\uB098, \uC544\uC9C1 \uBAA8\uB4E0 \uC790\uC5F0\uC218\uC5D0 \uB300\uD55C \uC99D\uBA85\uC740 \uBC1C\uACAC\uB418\uC9C0 \uC54A\uACE0 \uC788\uB2E4. \uC774 \uBB38\uC81C\uC758 \uD574\uACB0\uC5D0 500\uB2EC\uB7EC\uC758 \uD604\uC0C1\uAE08\uC744 \uAC78\uC5C8\uB358 \uC5D0\uB974\uB418\uC2DC \uD314\uC740 \"\uC218\uD559\uC740 \uC544\uC9C1 \uC774\uB7F0 \uBB38\uC81C\uB97C \uB2E4\uB8F0 \uC900\uBE44\uAC00 \uB418\uC5B4 \uC788\uC9C0 \uC54A\uB2E4.\"\uB294 \uB9D0\uC744 \uB0A8\uACBC\uB2E4. \uB2E4\uC74C\uACFC \uAC19\uC740 \uD1B5\uACC4\uC801\uC778 \uC124\uBA85\uC744 \uC0DD\uAC01\uD558\uBA74 \uC774 \uCD94\uCE21\uC740 \uCC38\uC77C \uAC00\uB2A5\uC131\uC774 \uB192\uC544 \uBCF4\uC778\uB2E4. \uADF8\uB7EC\uB098 \uC774\uAC83\uC774 \uCF5C\uB77C\uCE20 \uCD94\uCE21\uC744 \uC99D\uBA85\uD558\uB294 \uAC83\uC740 \uC544\uB2C8\uB2E4. \uC774 \uC870\uC791\uC5D0 \uC758\uD574 \uB9CC\uB4E4\uC5B4\uC9C0\uB294 \uD640\uC218\uB4E4\uB9CC \uC0DD\uAC01\uD558\uBA74, \uB2E4\uC74C\uC5D0 \uC624\uB294 \uD640\uC218\uB294 \uD3C9\uADE0\uC801\uC73C\uB85C \uADF8 \uC804\uC758 \uC218\uC758 3/4\uC815\uB3C4\uC758 \uAC12\uC744 \uAC16\uB294\uB2E4. \uB530\uB77C\uC11C \uD640\uC218\uC758 \uC218\uC5F4\uC740 \uC810\uC810 \uC791\uC544\uC838 \uACB0\uAD6D 1\uC774 \uB420 \uAC83\uC774\uB2E4."@ko . . . "1124758356"^^ . . . "Vermoeden van Collatz"@nl . . "La conjectura de Collatz \u00E9s un dels problemes no resolts m\u00E9s famosos de les matem\u00E0tiques. La conjectura es pregunta si repetir dues operacions aritm\u00E8tiques simples acabar\u00E0 transformant cada nombre enter positiu en 1. Es tracta de seq\u00FC\u00E8ncies de nombres enters en qu\u00E8 cada terme s'obt\u00E9 del terme anterior de la seg\u00FCent manera: si el terme anterior \u00E9s parell, el terme seg\u00FCent \u00E9s la meitat del terme anterior. Si el terme anterior \u00E9s senar, el seg\u00FCent \u00E9s 3 vegades el terme anterior m\u00E9s 1. La conjectura \u00E9s que aquestes seq\u00FC\u00E8ncies sempre arriben a 1, independentment del nombre enter positiu que s'esculli per iniciar la seq\u00FC\u00E8ncia. Aquesta conjuectura porta el nom del matem\u00E0tic Lothar Collatz, que va presentar la idea l'any 1937, dos anys despr\u00E9s de doctorar-se. Tamb\u00E9 es coneix com el problema 3n + 1, la conjectura 3n + 1, la conjectura d'Ulam (per Stanis\u0142aw Ulam), el problema de Kakutani (per Shizuo Kakutani), la conjectura de Thwaites (per ), l'algoritme de Hasse (per Helmut Hasse), o el problema de Syracuse (per la Universitat americana de Syracuse que hi va dedicar molts esfor\u00E7os). La seq\u00FC\u00E8ncia de n\u00FAmeros implicada de vegades es coneix com a seq\u00FC\u00E8ncia de calamarsa, n\u00FAmeros de calamarsa o n\u00FAmerals de calamarsa (perqu\u00E8 els valors solen estar subjectes a m\u00FAltiples baixades i ascensos com la calamarsa en un n\u00FAvol), o com a nombres meravellosos. Paul Erd\u0151s va dir sobre la conjectura de Collatz: \u00ABLes matem\u00E0tiques potser no estan preparades per a aquests problemes\u00BB. Tamb\u00E9 va oferir 500 US$ per la seva soluci\u00F3. Jeffrey Lagarias va afirmar el 2010 que la conjectura de Collatz \u00AB\u00E9s un problema extraordin\u00E0riament dif\u00EDcil, completament fora de l'abast de les matem\u00E0tiques actuals\u00BB."@ca . . "Das Collatz-Problem, auch als (3n+1)-Vermutung bezeichnet, ist ein ungel\u00F6stes mathematisches Problem, das 1937 von Lothar Collatz gestellt wurde. Es hat Verbindungen zur Zahlentheorie, zur Theorie dynamischer Systeme und Ergodentheorie und zur Theorie der Berechenbarkeit in der Informatik. Das Problem gilt als notorisch schwierig, obwohl es einfach zu formulieren ist. Jeffrey Lagarias, der als Experte f\u00FCr das Problem gilt, zitiert eine m\u00FCndliche Mitteilung von Paul Erd\u0151s, der es als \u201Eabsolut hoffnungslos\u201C bezeichnete."@de . . . . . . "Konjektur Collatz"@in . "Problem Collatza (znany te\u017C jako problem 3x+1, problem Ulama, problem Kakutaniego, problem syrakuza\u0144ski) \u2013 nierozstrzygni\u0119ty dotychczas problem o wyj\u0105tkowo prostym \u2013 jak wiele innych problem\u00F3w teorii liczb \u2013 sformu\u0142owaniu. Nazwa pochodzi od nazwiska niemieckiego matematyka Lothara Collatza (1937). Zagadnienie to by\u0142o r\u00F3wnie\u017C rozpatrywane przez polskiego matematyka Stanis\u0142awa Ulama, a tak\u017Ce przez ."@pl . . . . "La conjetura de Collatz, conocida tambi\u00E9n como conjetura 3n+1 o conjetura de Ulam (entre otros nombres), fue enunciada por el matem\u00E1tico Lothar Collatz en 1937, y a la fecha no se ha resuelto."@es . . . . . . . . . . "Collatz problem"@sv . . . . . . . . . "Konjekto de Collatz"@eo . . . . "\u30B3\u30E9\u30C3\u30C4\u306E\u554F\u984C\uFF08\u30B3\u30E9\u30C3\u30C4\u306E\u3082\u3093\u3060\u3044\u3001Collatz problem\uFF09\u306F\u3001\u6570\u8AD6\u306E\u672A\u89E3\u6C7A\u554F\u984C\u306E\u3072\u3068\u3064\u3067\u3042\u308B\u3002\u554F\u984C\u306E\u7D50\u8AD6\u306E\u4E88\u60F3\u3092\u6307\u3057\u3066\u30B3\u30E9\u30C3\u30C4\u4E88\u60F3\u3068\u8A00\u3046\u3002\u4F1D\u7D71\u7684\u306B\u30ED\u30FC\u30BF\u30FC\u30FB\u30B3\u30E9\u30C3\u30C4\u306E\u540D\u3092\u51A0\u3055\u308C\u3066\u547C\u3070\u308C\u308B\u304C\u3001\u56FA\u6709\u540D\u8A5E\u306B\u4F9D\u62E0\u3057\u306A\u3044\u8868\u73FE\u3068\u3057\u3066\u306F3n+1\u554F\u984C\u3068\u3082\u8A00\u308F\u308C\u3001\u307E\u305F\u521D\u671F\u306B\u3053\u306E\u554F\u984C\u306B\u53D6\u308A\u7D44\u3093\u3060\u7814\u7A76\u8005\u306E\u540D\u3092\u51A0\u3057\u3066\u3001\u89D2\u8C37\u306E\u554F\u984C\u3001\u7C73\u7530\u306E\u4E88\u60F3\u3001\u30A6\u30E9\u30E0\u306E\u4E88\u60F3\u3001\u30B7\u30E9\u30AD\u30E5\u30FC\u30B9\u554F\u984C\u306A\u3069\u3068\u3082\u547C\u3070\u308C\u308B\u3002 \u6570\u5B66\u8005\u30DD\u30FC\u30EB\u30FB\u30A8\u30EB\u30C7\u30B7\u30E5\u306F\u300C\u6570\u5B66\u306F\u307E\u3060\u3053\u306E\u7A2E\u306E\u554F\u984C\u306B\u5BFE\u3059\u308B\u7528\u610F\u304C\u3067\u304D\u3066\u3044\u306A\u3044\u300D\u3068\u8FF0\u3079\u305F\u3002\u307E\u305F\u3001\u30B8\u30A7\u30D5\u30EA\u30FC\u30FB\u30E9\u30AC\u30EA\u30A2\u30B9\u306F2010\u5E74\u306B\u3001\u30B3\u30E9\u30C3\u30C4\u306E\u4E88\u60F3\u306F\u300C\u975E\u5E38\u306B\u96E3\u3057\u3044\u554F\u984C\u3067\u3042\u308A\u3001\u73FE\u4EE3\u306E\u6570\u5B66\u3067\u306F\u5B8C\u5168\u306B\u624B\u304C\u5C4A\u304B\u306A\u3044\u300D\u3068\u8FF0\u3079\u305F\u3002 2019\u5E7412\u6708\u3001\u30C6\u30EC\u30F3\u30B9\u30FB\u30BF\u30AA\u306F\u30B3\u30E9\u30C3\u30C4\u306E\u554F\u984C\u304C\u307B\u3068\u3093\u3069\u3059\u3079\u3066\u306E\u6B63\u306E\u6574\u6570\u306B\u304A\u3044\u3066\u307B\u3068\u3093\u3069\u6B63\u3057\u3044\u3068\u3059\u308B\u8AD6\u6587\u3092\u767A\u8868\u3057\u305F\u3002"@ja . "Conjetura de Collatz"@es . . . "La conjecture de Syracuse, encore appel\u00E9e conjecture de Collatz, conjecture d'Ulam, conjecture tch\u00E8que ou probl\u00E8me 3x + 1, est l'hypoth\u00E8se math\u00E9matique selon laquelle la suite de Syracuse de n'importe quel entier strictement positif atteint 1. Une suite de Syracuse est une suite d'entiers naturels d\u00E9finie de la mani\u00E8re suivante : on part d'un nombre entier strictement positif ; s\u2019il est pair, on le divise par 2 ; s\u2019il est impair, on le multiplie par 3 et l'on ajoute 1. En r\u00E9p\u00E9tant l\u2019op\u00E9ration, on obtient une suite d'entiers strictement positifs dont chacun ne d\u00E9pend que de son pr\u00E9d\u00E9cesseur."@fr . . . . . . "\u0397 \u03B5\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 \u03C4\u03BF\u03C5 \u039A\u03CC\u03BB\u03B1\u03C4\u03B6 (\u03B1\u03B3\u03B3\u03BB\u03B9\u03BA\u03AC: Collatz conjecture) \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BC\u03B9\u03B1 \u03B5\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 \u03C3\u03C4\u03B1 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03AC \u03B7 \u03BF\u03C0\u03BF\u03AF\u03B1 \u03C0\u03AE\u03C1\u03B5 \u03C4\u03B7\u03BD \u03BF\u03BD\u03BF\u03BC\u03B1\u03C3\u03AF\u03B1 \u03C4\u03B7\u03C2 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD (Lothar Collatz), \u03BF \u03BF\u03C0\u03BF\u03AF\u03BF\u03C2 \u03C4\u03B7\u03BD \u03C0\u03C1\u03CC\u03C4\u03B5\u03B9\u03BD\u03B5 \u03B3\u03B9\u03B1 \u03C0\u03C1\u03CE\u03C4\u03B7 \u03C6\u03BF\u03C1\u03AC \u03C4\u03BF 1937. \u0397 \u03B5\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B5\u03C0\u03AF\u03C3\u03B7\u03C2 \u03B3\u03BD\u03C9\u03C3\u03C4\u03AE \u03C9\u03C2 \u03B5\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 3n+1, \u03B5\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 \u039F\u03CD\u03BB\u03B1\u03BC \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD (Stanislaw Ulam), \u03C0\u03C1\u03CC\u03B2\u03BB\u03B7\u03BC\u03B1 \u039A\u03B1\u03BA\u03BF\u03C5\u03C4\u03AC\u03BD\u03B9 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD (Shizuo Kakutani), \u03B5\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 \u0398\u03BF\u03C5\u03AD\u03B9\u03C4\u03C2 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD (Bryan Thwaites), \u03B1\u03BB\u03B3\u03CC\u03C1\u03B9\u03B8\u03BC\u03BF\u03C2 \u03C4\u03BF\u03C5 \u03A7\u03AC\u03C3\u03B5 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD (Helmut Hasse), \u03AE \u03C0\u03C1\u03CC\u03B2\u03BB\u03B7\u03BC\u03B1 \u03C4\u03C9\u03BD \u03A3\u03C5\u03C1\u03B1\u03BA\u03BF\u03C5\u03C3\u03CE\u03BD. \u0397 \u03B1\u03BA\u03BF\u03BB\u03BF\u03C5\u03B8\u03AF\u03B1 \u03C4\u03C9\u03BD \u03B1\u03C1\u03B9\u03B8\u03BC\u03CE\u03BD \u03C0\u03BF\u03C5 \u03B5\u03BC\u03C0\u03BB\u03AD\u03BA\u03BF\u03BD\u03C4\u03B1\u03B9 \u03B1\u03BD\u03B1\u03C6\u03AD\u03C1\u03B5\u03C4\u03B1\u03B9 \u03C9\u03C2 \u03B1\u03BA\u03BF\u03BB\u03BF\u03C5\u03B8\u03AF\u03B1 \u03C7\u03B1\u03BB\u03B1\u03B6\u03B9\u03BF\u03CD (\u03B5\u03C0\u03B5\u03B9\u03B4\u03AE \u03BF\u03B9 \u03C4\u03B9\u03BC\u03AD\u03C2 \u03C3\u03C5\u03BD\u03AE\u03B8\u03C9\u03C2 \u03C5\u03C0\u03CC\u03BA\u03B5\u03B9\u03BD\u03C4\u03B1\u03B9 \u03C3\u03B5 \u03C0\u03BF\u03BB\u03BB\u03B1\u03C0\u03BB\u03AD\u03C2 \u03BA\u03B1\u03C4\u03B1\u03B2\u03AC\u03C3\u03B5\u03B9\u03C2 \u03BA\u03B1\u03B9 \u03B1\u03BD\u03B1\u03B2\u03AC\u03C3\u03B5\u03B9\u03C2 \u03C3\u03B1\u03BD \u03C4\u03BF\u03C5\u03C2 \u03BA\u03CC\u03BA\u03BA\u03BF\u03C5\u03C2 \u03C4\u03BF\u03C5 \u03C7\u03B1\u03BB\u03B1\u03B6\u03B9\u03BF\u03CD \u03C3\u03B5 \u03AD\u03BD\u03B1 \u03C3\u03CD\u03BD\u03BD\u03B5\u03C6\u03BF, \u03B5\u03AF\u03C4\u03B5 \u03C9\u03C2 \u03B8\u03B1\u03C5\u03BC\u03B1\u03C3\u03C4\u03BF\u03AF \u03B1\u03C1\u03B9\u03B8\u03BC\u03BF\u03AF. \u0397 \u03B5\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 \u03C3\u03C5\u03BD\u03BF\u03C8\u03AF\u03B6\u03B5\u03C4\u03B1\u03B9 \u03C9\u03C2 \u03B5\u03BE\u03AE\u03C2. \u03A0\u03AC\u03C1\u03C4\u03B5 \u03BF\u03C0\u03BF\u03B9\u03BF\u03B4\u03AE\u03C0\u03BF\u03C4\u03B5 \u03B8\u03B5\u03C4\u03B9\u03BA\u03CC \u03B1\u03BA\u03AD\u03C1\u03B1\u03B9\u03BF n. \u0391\u03BD \u03BF n \u03B5\u03AF\u03BD\u03B1\u03B9 \u03AC\u03C1\u03C4\u03B9\u03BF\u03C2, \u03B4\u03B9\u03B1\u03B9\u03C1\u03AD\u03C3\u03C4\u03B5 \u03C4\u03BF\u03BD \u03B4\u03B9\u03B1 \u03C4\u03BF 2, \u03B3\u03B9\u03B1 \u03BD\u03B1 \u03C0\u03AC\u03C1\u03B5\u03C4\u03B5 \u03C4\u03BF n/2. \u0395\u03AC\u03BD \u03BF n \u03B5\u03AF\u03BD\u03B1\u03B9 \u03C0\u03B5\u03C1\u03B9\u03C4\u03C4\u03CC\u03C2, \u03C0\u03BF\u03BB\u03BB\u03B1\u03C0\u03BB\u03B1\u03C3\u03B9\u03AC\u03C3\u03C4\u03B5 \u03C4\u03BF\u03BD \u03B5\u03C0\u03AF 3 \u03BA\u03B1\u03B9 \u03C0\u03C1\u03BF\u03C3\u03B8\u03AD\u03C3\u03C4\u03B5 1 \u03B3\u03B9\u03B1 \u03BD\u03B1 \u03C0\u03AC\u03C1\u03B5\u03C4\u03B5 \u03C4\u03BF 3n+1. \u0395\u03C0\u03B1\u03BD\u03B1\u03BB\u03AC\u03B2\u03B5\u03C4\u03B5 \u03C4\u03B7 \u03B4\u03B9\u03B1\u03B4\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 (\u03B7 \u03BF\u03C0\u03BF\u03AF\u03B1 \u03AD\u03C7\u03B5\u03B9 \u03C7\u03B1\u03C1\u03B1\u03BA\u03C4\u03B7\u03C1\u03B9\u03C3\u03C4\u03B5\u03AF \u03C9\u03C2 \"\u039C\u03B9\u03C3\u03CC \u0389 \u03A4\u03C1\u03B9\u03C0\u03BB\u03CC \u03A3\u03C5\u03BD \u0388\u03BD\u03B1\", \u03B1\u03B3\u03B3\u03BB\u03B9\u03BA\u03AC \"Half Or Triple Plus One, HOTPO) \u03B5\u03C0' \u03B1\u03CC\u03C1\u03B9\u03C3\u03C4\u03BF\u03BD. \u039A\u03B1\u03C4\u03AC \u03C4\u03B7\u03BD \u03B5\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1, \u03B1\u03C0\u03CC \u03CC\u03C0\u03BF\u03B9\u03BF \u03B1\u03C1\u03B9\u03B8\u03BC\u03CC \u03BA\u03B9 \u03B1\u03BD \u03BE\u03B5\u03BA\u03B9\u03BD\u03AE\u03C3\u03B5\u03C4\u03B5, \u03B8\u03B1 \u03BA\u03B1\u03C4\u03B1\u03BB\u03AE\u03BE\u03B5\u03C4\u03B5 \u03C0\u03AC\u03BD\u03C4\u03B1 \u03C3\u03C4\u03BF \u03AD\u03BD\u03B1. \u039F \u03A0\u03C9\u03BB \u0388\u03C1\u03BD\u03C4\u03BF\u03C2 \u03B4\u03AE\u03BB\u03C9\u03C3\u03B5 \u03C3\u03C7\u03B5\u03C4\u03B9\u03BA\u03AC \u03BC\u03B5 \u03C4\u03B7\u03BD \u03B5\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 \u03C4\u03BF\u03C5 \u039A\u03CC\u03BB\u03B1\u03C4\u03B6: \"\u03A4\u03B1 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03AC \u03BC\u03C0\u03BF\u03C1\u03B5\u03AF \u03BD\u03B1 \u03BC\u03B7\u03BD \u03B5\u03AF\u03BD\u03B1\u03B9 \u03AD\u03C4\u03BF\u03B9\u03BC\u03B1 \u03B3\u03B9\u03B1 \u03C4\u03AD\u03C4\u03BF\u03B9\u03B1 \u03C0\u03C1\u03BF\u03B2\u03BB\u03AE\u03BC\u03B1\u03C4\u03B1.\" \u0395\u03C0\u03AF\u03C3\u03B7\u03C2, \u03C0\u03C1\u03CC\u03C3\u03C6\u03B5\u03C1\u03B5 $500 \u03B3\u03B9\u03B1 \u03C4\u03B7\u03BD \u03BB\u03CD\u03C3\u03B7 \u03C4\u03BF\u03C5."@el . . . "Das Collatz-Problem, auch als (3n+1)-Vermutung bezeichnet, ist ein ungel\u00F6stes mathematisches Problem, das 1937 von Lothar Collatz gestellt wurde. Es hat Verbindungen zur Zahlentheorie, zur Theorie dynamischer Systeme und Ergodentheorie und zur Theorie der Berechenbarkeit in der Informatik. Das Problem gilt als notorisch schwierig, obwohl es einfach zu formulieren ist. Jeffrey Lagarias, der als Experte f\u00FCr das Problem gilt, zitiert eine m\u00FCndliche Mitteilung von Paul Erd\u0151s, der es als \u201Eabsolut hoffnungslos\u201C bezeichnete."@de . . . . "\u0413\u0456\u043F\u043E\u0442\u0435\u0437\u0430 \u041A\u043E\u043B\u043B\u0430\u0442\u0446\u0430 (\u0433\u0456\u043F\u043E\u0442\u0435\u0437\u0430 3n+1, \u0433\u0456\u043F\u043E\u0442\u0435\u0437\u0430 3x+1, \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 \u041A\u043E\u043B\u043B\u0430\u0442\u0446\u0430, \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 3n+1, \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430 3x+1, \u0421\u0456\u0440\u0430\u043A\u0443\u0437\u044C\u043A\u0430 \u043F\u0440\u043E\u0431\u043B\u0435\u043C\u0430) \u2014 \u043E\u0434\u043D\u0430 \u0437 \u043D\u0435\u0440\u043E\u0437\u0432'\u044F\u0437\u0430\u043D\u0438\u0445 \u043F\u0440\u043E\u0431\u043B\u0435\u043C \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438, \u043D\u0430\u0437\u0432\u0430\u043D\u0430 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u043D\u0456\u043C\u0435\u0446\u044C\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u041B\u043E\u0442\u0430\u0440\u0430 \u041A\u043E\u043B\u043B\u0430\u0442\u0446\u0430, \u044F\u043A\u0438\u0439 \u0437\u0430\u043F\u0440\u043E\u043F\u043E\u043D\u0443\u0432\u0430\u0432 \u0457\u0457 \u0443 1937 \u0440\u043E\u0446\u0456."@uk . . . . . . . . . . . . "\u8003\u62C9\u5179\u731C\u60F3\uFF08\u82F1\u8A9E\uFF1ACollatz conjecture\uFF09\uFF0C\u53C8\u79F0\u4E3A\u5947\u5076\u5F52\u4E00\u731C\u60F3\u30013n+1\u731C\u60F3\u3001\u51B0\u96F9\u731C\u60F3\u3001\u89D2\u8C37\u731C\u60F3\u3001\u54C8\u585E\u731C\u60F3\u3001\u4E4C\u62C9\u59C6\u731C\u60F3\u6216\u53D9\u62C9\u53E4\u731C\u60F3\uFF0C\u662F\u6307\u5BF9\u4E8E\u6BCF\u4E00\u4E2A\u6B63\u6574\u6570\uFF0C\u5982\u679C\u5B83\u662F\u5947\u6570\uFF0C\u5219\u5BF9\u5B83\u4E583\u518D\u52A01\uFF0C\u5982\u679C\u5B83\u662F\u5076\u6570\uFF0C\u5219\u5BF9\u5B83\u9664\u4EE52\uFF0C\u5982\u6B64\u5FAA\u73AF\uFF0C\u6700\u7EC8\u90FD\u80FD\u591F\u5F97\u52301\u3002"@zh . . . . . "\u0413\u0456\u043F\u043E\u0442\u0435\u0437\u0430 \u041A\u043E\u043B\u043B\u0430\u0442\u0446\u0430"@uk . "Collatz Problem"@en . . . "Collatz aieru"@eu . "La congettura di Collatz (conosciuta anche come congettura 3n + 1, congettura di Syracuse, congettura di Ulam o numeri di Hailstone) \u00E8 una congettura matematica tuttora irrisolta. Fu enunciata per la prima volta nel 1937 da Lothar Collatz, da cui prende il nome. Paul Erd\u0151s disse, circa questa congettura, che \u00ABla matematica non \u00E8 ancora matura per problemi di questo tipo\u00BB, e offr\u00EC 500 dollari per la sua soluzione."@it . . . . . . "\u0413\u0438\u043F\u043E\u0442\u0435\u0437\u0430 \u041A\u043E\u043B\u043B\u0430\u0442\u0446\u0430"@ru . "\u0397 \u03B5\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 \u03C4\u03BF\u03C5 \u039A\u03CC\u03BB\u03B1\u03C4\u03B6 (\u03B1\u03B3\u03B3\u03BB\u03B9\u03BA\u03AC: Collatz conjecture) \u03B5\u03AF\u03BD\u03B1\u03B9 \u03BC\u03B9\u03B1 \u03B5\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 \u03C3\u03C4\u03B1 \u03BC\u03B1\u03B8\u03B7\u03BC\u03B1\u03C4\u03B9\u03BA\u03AC \u03B7 \u03BF\u03C0\u03BF\u03AF\u03B1 \u03C0\u03AE\u03C1\u03B5 \u03C4\u03B7\u03BD \u03BF\u03BD\u03BF\u03BC\u03B1\u03C3\u03AF\u03B1 \u03C4\u03B7\u03C2 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD (Lothar Collatz), \u03BF \u03BF\u03C0\u03BF\u03AF\u03BF\u03C2 \u03C4\u03B7\u03BD \u03C0\u03C1\u03CC\u03C4\u03B5\u03B9\u03BD\u03B5 \u03B3\u03B9\u03B1 \u03C0\u03C1\u03CE\u03C4\u03B7 \u03C6\u03BF\u03C1\u03AC \u03C4\u03BF 1937. \u0397 \u03B5\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03B5\u03C0\u03AF\u03C3\u03B7\u03C2 \u03B3\u03BD\u03C9\u03C3\u03C4\u03AE \u03C9\u03C2 \u03B5\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 3n+1, \u03B5\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 \u039F\u03CD\u03BB\u03B1\u03BC \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD (Stanislaw Ulam), \u03C0\u03C1\u03CC\u03B2\u03BB\u03B7\u03BC\u03B1 \u039A\u03B1\u03BA\u03BF\u03C5\u03C4\u03AC\u03BD\u03B9 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD (Shizuo Kakutani), \u03B5\u03B9\u03BA\u03B1\u03C3\u03AF\u03B1 \u0398\u03BF\u03C5\u03AD\u03B9\u03C4\u03C2 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD (Bryan Thwaites), \u03B1\u03BB\u03B3\u03CC\u03C1\u03B9\u03B8\u03BC\u03BF\u03C2 \u03C4\u03BF\u03C5 \u03A7\u03AC\u03C3\u03B5 \u03B1\u03C0\u03CC \u03C4\u03BF\u03BD (Helmut Hasse), \u03AE \u03C0\u03C1\u03CC\u03B2\u03BB\u03B7\u03BC\u03B1 \u03C4\u03C9\u03BD \u03A3\u03C5\u03C1\u03B1\u03BA\u03BF\u03C5\u03C3\u03CE\u03BD. \u0397 \u03B1\u03BA\u03BF\u03BB\u03BF\u03C5\u03B8\u03AF\u03B1 \u03C4\u03C9\u03BD \u03B1\u03C1\u03B9\u03B8\u03BC\u03CE\u03BD \u03C0\u03BF\u03C5 \u03B5\u03BC\u03C0\u03BB\u03AD\u03BA\u03BF\u03BD\u03C4\u03B1\u03B9 \u03B1\u03BD\u03B1\u03C6\u03AD\u03C1\u03B5\u03C4\u03B1\u03B9 \u03C9\u03C2 \u03B1\u03BA\u03BF\u03BB\u03BF\u03C5\u03B8\u03AF\u03B1 \u03C7\u03B1\u03BB\u03B1\u03B6\u03B9\u03BF\u03CD (\u03B5\u03C0\u03B5\u03B9\u03B4\u03AE \u03BF\u03B9 \u03C4\u03B9\u03BC\u03AD\u03C2 \u03C3\u03C5\u03BD\u03AE\u03B8\u03C9\u03C2 \u03C5\u03C0\u03CC\u03BA\u03B5\u03B9\u03BD\u03C4\u03B1\u03B9 \u03C3\u03B5 \u03C0\u03BF\u03BB\u03BB\u03B1\u03C0\u03BB\u03AD\u03C2 \u03BA\u03B1\u03C4\u03B1\u03B2\u03AC\u03C3\u03B5\u03B9\u03C2 \u03BA\u03B1\u03B9 \u03B1\u03BD\u03B1\u03B2\u03AC\u03C3\u03B5\u03B9\u03C2 \u03C3\u03B1\u03BD \u03C4\u03BF\u03C5\u03C2 \u03BA\u03CC\u03BA\u03BA\u03BF\u03C5\u03C2 \u03C4\u03BF\u03C5 \u03C7\u03B1\u03BB\u03B1\u03B6\u03B9\u03BF\u03CD \u03C3\u03B5 \u03AD\u03BD\u03B1 \u03C3\u03CD\u03BD\u03BD\u03B5\u03C6\u03BF, \u03B5\u03AF\u03C4\u03B5 \u03C9\u03C2 \u03B8\u03B1\u03C5\u03BC\u03B1\u03C3\u03C4\u03BF\u03AF \u03B1\u03C1\u03B9\u03B8\u03BC\u03BF\u03AF."@el . . . . . .