Pisano Period
In number theory, the ''n''th Pisano period, written as '(''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. Definition The Fibonacci numbers are the numbers in the integer sequence: :0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, ... defined by the recurrence relation :F_0 = 0 :F_1 = 1 :F_i = F_ + F_. For any integer ''n'', the sequence of Fibonacci numbers ''Fi'' taken modulo ''n'' is periodic. The Pisano period, denoted '(''n''), is the length of the period of this sequence. For example, the sequence of Fibonacci numbers modulo 3 begins: :0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, ... This sequence has period 8, so '(3) = 8. Properties Parity Wit ...
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Pisano Periods
Pisano may refer to: * Pisano, a native or inhabitant of Pisa, Italy * Pisano (surname), a list of people * Pisano, Piedmont, commune in the province of Novara, in northern Italy * Pisano period, in number theory * Pisanello (1380–1456), Italian artist sometimes erroneously called Vittore Pisano See also

* * Pisa (other) * Pisana (other) * Pisani (other) * Pisanu, a surname {{disambiguation ...
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