Factorial divisible by Mersenn Numbers
Find all positive integer $n$ so that $n!$ is divisible by $2^n-1$.
One one thing is neutral in the universe, that is $0$.
Re: Factorial divisible by Mersenn Numbers
Bang's theorem tells us that if $n\neq 1,6$ then $2^n-1$ has a primitive prime divisor $p$. If $p\le n$ then $p$ divides $2^{p-1}-1$ which is less than $2^n-1$, a contradiction. So one only needs to check $n=1,6$ of which only $n=1$ works.
"Everything should be made as simple as possible, but not simpler." - Albert Einstein