Let $p$ and $q=4p+1$ be prime numbers. Determine the least power $i$ of 2 for which $2^i\equiv 1\,(mod\, q)$.
Problem
Source: III International Festival of Young Mathematicians Sozopol 2012, Theme for 10-12 grade
Tags: number theory, modulo
Source: III International Festival of Young Mathematicians Sozopol 2012, Theme for 10-12 grade
Tags: number theory, modulo
Let $p$ and $q=4p+1$ be prime numbers. Determine the least power $i$ of 2 for which $2^i\equiv 1\,(mod\, q)$.