The easiest unsolved math problem

Consider any prime number $latex p$. Compute $latex 2^{p-1}-1$. For example, if $latex p$ is 11, this makes 1023. Now take the number 1023 and divide it by $latex p$ (11). Do we get an exact integer? Yes, we get 93. (And we will always get an integer, by Fermat's Little Theorem.) Now take that …