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dbr:Prouhet–Tarry–Escott_problem
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Problème de Prouhet-Tarry-Escott 等冪和問題 Prouhet–Tarry–Escott problem
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En mathématiques, et plus particulièrement en théorie des nombres et en combinatoire, le problème de Prouhet-Tarry-Escott est de trouver, pour chaque entier , deux ensembles et de entiers chacun, tel que : pour chaque de jusqu'à un entier donné. Si et vérifient ces conditions, on écrit . On cherche une solution de taille minimale pour un degré donné. Ce problème, toujours ouvert, est nommé d'après Eugène Prouhet, qui l'a étudié en 1851, et Gaston Tarry et Edward Brind Escott, qui l'ont considéré au début des années 1910. In mathematics, the Prouhet–Tarry–Escott problem asks for two disjoint multisets A and B of n integers each, whose first k power sum symmetric polynomials are all equal.That is, the two multisets should satisfy the equations for each integer i from 1 to a given k. It has been shown that n must be strictly greater than k. Solutions with are called ideal solutions. Ideal solutions are known for and for . No ideal solution is known for or for . 等冪和問題是數論中一個有趣的問題，所謂等冪和即將左右不全等的等式兩邊各數字做同次方(冪)並相加後，能使等式成立，即能滿足下方一系列等式者，稱作「等冪和」。…… （以上所有數皆屬於整數） 關於這類數組的規律，尚無清楚且公認解答。目前已知最大的解为A = {±22, ±61, ±86, ±127, ±140, ±151}，B = {±35, ±47, ±94, ±121, ±146, ±148}，k=11。
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Prouhet-Tarry-Escott problem
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Prouhet-Tarry-EscottProblem
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等冪和問題是數論中一個有趣的問題，所謂等冪和即將左右不全等的等式兩邊各數字做同次方(冪)並相加後，能使等式成立，即能滿足下方一系列等式者，稱作「等冪和」。…… （以上所有數皆屬於整數） 關於這類數組的規律，尚無清楚且公認解答。目前已知最大的解为A = {±22, ±61, ±86, ±127, ±140, ±151}，B = {±35, ±47, ±94, ±121, ±146, ±148}，k=11。 En mathématiques, et plus particulièrement en théorie des nombres et en combinatoire, le problème de Prouhet-Tarry-Escott est de trouver, pour chaque entier , deux ensembles et de entiers chacun, tel que : pour chaque de jusqu'à un entier donné. Si et vérifient ces conditions, on écrit . On cherche une solution de taille minimale pour un degré donné. Ce problème, toujours ouvert, est nommé d'après Eugène Prouhet, qui l'a étudié en 1851, et Gaston Tarry et Edward Brind Escott, qui l'ont considéré au début des années 1910. La plus grande valeur de pour laquelle on connaît une solution avec est . Une solution correspondante est donnée par les ensembles suivants : In mathematics, the Prouhet–Tarry–Escott problem asks for two disjoint multisets A and B of n integers each, whose first k power sum symmetric polynomials are all equal.That is, the two multisets should satisfy the equations for each integer i from 1 to a given k. It has been shown that n must be strictly greater than k. Solutions with are called ideal solutions. Ideal solutions are known for and for . No ideal solution is known for or for . This problem was named after , who studied it in the early 1850s, and Gaston Tarry and Edward B. Escott, who studied it in the early 1910s. The problem originates from letters of Christian Goldbach and Leonhard Euler (1750/1751).
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