Pisano period

Pisano period is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The Fibonacci sequence taken modulo 2 is a periodic sequence of period 3 : 0, 1, 1, 0, 1, 1, ...

For any integer n, the Fibonacci sequence taken modulo n is periodic and the period is called the Pisano period.

Let call Pisano, the Pisano period (Pisano(2) = 3). If m and n are coprime, Pisano(m*n) = lcm(Pisano(m),Pisano(n)).

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.

Task

Write 2 functions: pisanoPrime(p,k) and pisano(m).

pisanoPrime(p,k) return the Pisano period of p^k where p is prime and k is a positive integer.

pisano(m) uses pisanoPrime to return the Pisano period of m where m is a positive integer.

Print pisanoPrime(p,1) and pisanoPrime(p,2) for every prime lower than 100.

Print pisano(m) for every integer from 2 to 200.

Related tasks

•  Fibonacci sequence
•  Prime decomposition
•  Least common multiple