# Modular Fibonacci series

My second observation is the following. Let $p$ be a prime not equal to $5$. Then $5$ is a quadratic residue modulo $p$ if and only if $p\equiv\pm1\pmod5$. And $5$ is not a quadratic residue modulo $p$ if and only if $p\equiv\pm2\pmod5$.

If $p$ is a prime and $m$ the period of $F_n\pmod{p}$, then $p\equiv\pm1\pmod5$ implies $m|(p-1)$.

I am looking for a generalization of the above cited statment.

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Hello! thank you so much for editing my question, which I faild to type. – pavani.neta Sep 13 '11 at 6:32