PAMO 2025 Problem 3

A positive integer $N$ with $m$ digits is called $a$ $repetitive$ $number$ $with$ $m$ $digits$ if the number formed by the last $m$ digits of $N^k$ is always $N$ for all positive integer $k$ . For example $5$ is a $repetitive$ $number$ $with$ $1$ $digit$ . Find all $repetitive$ $numbers$ $with$ $6$ $digits$ .