Calculating Pisano periods for any integer

Question

I recently stumbled across this SPOJ question:

http://www.spoj.com/problems/PISANO/ The question is simple. Calculate the Pisano period of a number. After I researched my way through the web, I found that a number's Pisano period can be calculated in terms of its prime factors. For prime numbers we have another method which uses Binet's formula. Is there any alternative for solving this problem?

Answer 1

Let p be a prime number > 5. If p is 1 or 4 in the modulus of 5, then the Pisano period is a divisor of p-1. If p is 2 or 3 in the modulus of 5, then the Pisano period is a divisor of 2p+2.