About: Pisano period

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In number theory, the nth Pisano period, written as π(n), is the period with which the sequence of Fibonacci numbers taken modulo n repeats. Pisano periods are named after Leonardo Pisano, better known as Fibonacci. The existence of periodic functions in Fibonacci numbers was noted by Joseph Louis Lagrange in 1774.

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rdf:type	yago:Abstraction100002137 yago:Amount105107765 yago:Attribute100024264 yago:Magnitude105090441 yago:Number105121418 yago:Property104916342 country yago:WikicatFibonacciNumbers
rdfs:label	Període de Pisano (ca) Période de Pisano (fr) Pisano period (en) Период Пизано (ru) 皮萨诺周期 (zh) Період Пізано (uk)
rdfs:comment	En teoria de nombres, el període de Pisano essent n qualsevol nombre enter, és la funció periòdica resultant d'aplicar un mòdul n a la successió de Fibonacci. Rep el nom de Leonardo Pisano, més conegut com a Fibonacci, i va ser descrit per Joseph Louis Lagrange l'any 1774. (ca) In number theory, the nth Pisano period, written as π(n), is the period with which the sequence of Fibonacci numbers taken modulo n repeats. Pisano periods are named after Leonardo Pisano, better known as Fibonacci. The existence of periodic functions in Fibonacci numbers was noted by Joseph Louis Lagrange in 1774. (en) Период Пизано — это длина периода последовательности Фибоначчи по модулю заданного натурального числа m. (ru) Період Пізано — це довжина періоду послідовності Фібоначчі за модулем заданого цілого додатного числа m. (uk) 在数论当中，自然数 n 的皮萨诺周期（通常记为π(n)）是斐波那契数列模 n 后的周期，以意大利数学家莱昂纳多·皮萨诺（即斐波那契）的名字命名。斐波那契数列取模後，周期的存在性曾在1774年为约瑟夫·拉格朗日所提及。 (zh) En théorie des nombres, la -ième période de Pisano, notée , est la longueur de la période à partir de laquelle la suite de Fibonacci, modulo se répète. Par exemple, la suite de Fibonacci modulo 3 est 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, etc. avec les huit premiers chiffres se répétant donc π(3) = 8. On peut montrer, en utilisant le Théorème chinois que, si sont premiers entre eux, alors , on se ramène ainsi à connaître les pour premier et entier non nul. En outre divise . Il n'est, par contre, pas connu s'il y a égalité entre ces deux quantités pour tous les . (fr)
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dcterms:subject	Fibonacci numbers Modular arithmetic
Wikipage page ID	1127427 (xsd:integer)
Wikipage revision ID	1122161245 (xsd:integer)
Link from a Wikipage to another Wikipage	6 (number) 8 (number) Prime power Quadratic extension Multiplicative order Totient 20 (number) Binet's formula University of Nottingham Duke Mathematical Journal Integer sequence Jacobsthal number 10 (number) 12 (number) 16 (number) Matrix (mathematics) General linear group Generalizations of Fibonacci numbers Pell number Quadratic residue Fibonacci numbers Modular arithmetic Zero divisor Parity (mathematics) 1 60 (number) Modular arithmetic Divisor Algebraic number theory 24 (number) Cyclic group Fibonacci Fibonacci number Finite field Number theory Quadratic reciprocity Recurrence relation Hexadecimal Invertible matrix Counterexample Prime number Chinese remainder theorem Least common multiple Zero of a function Joseph-Louis Lagrange 3 Coprime Group of units Integer Metallic mean Natural number OEIS Order (group theory) Sequence Lucas number Tetranacci number Finite ring Wall–Sun–Sun prime Integers modulo n Periodic function Frobenius automorphism Tribonacci number Prime factorization
Link from a Wikipage to an external page	http://webbox.lafayette.edu/~reiterc/nt/qr_fib_ec_preprint.pdf http://webspace.ship.edu/msrenault/fibonacci/fib.htm http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibmaths.html%23section6 http://www.dur.ac.uk/bob.johnson/fibonacci/
sameAs	Pisano period Pisano period Pisano period Pisano period Pisano period Pisano period Pisano period

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