Fermat's little theorem states that for a prime $$$p$$$ and any integer $$$a$$$ such that $$$0 < a < p$$$,

In other words, the powers of $$$a$$$ modulo $$$p$$$ repeat with a period of $$$p-1$$$.

This is further generalized by Euler's theorem which implies the powers of $$$a$$$ repeat with a period of $$$p-1$$$. This can be even further generalized with Lagrange's theorem for groups.

https://www.geeksforgeeks.org/find-abm-where-b-is-very-large/

You can use above link for better understanding.