Pisano period: Difference between revisions
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For any integer n, the Fibonacci sequence taken modulo n is periodic and the period is called the [[wp:Pisano_period|Pisano period]]. |
For any integer n, the Fibonacci sequence taken modulo n is periodic and the period is called the [[wp:Pisano_period|Pisano period]]. |
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Let call pisano, the Pisano period (pisano(2) = 3). If m and n are coprime, pisano(m*n) = lcm(pisano(m),pisano(n)). |
Let call pisano, the Pisano period (pisano(2) = 3). If m and n are [[wp:Coprime integers|coprime]], pisano(m*n) = [[wp:Least common multiple|lcm]](pisano(m),pisano(n)). |
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Therefore calculate the Pisano period of an integer m is accomplished by calculating the Pisano periods of the prime powers in the prime decomposition of m. |
Therefore calculate the Pisano period of an integer m is accomplished by calculating the Pisano periods of the prime powers in the prime decomposition of m. |
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