Hi I'm stuck with two questions:
(1). Prove that if $a^{n-1}\equiv 1 \pmod n$ then $a$ and $n$ are relatively prime.
looks like Fermat little theorem but I know this theory works on prime numbers so I tried to prove this using Euler function but I don't think this is the correct way.
(2). $p$ is prime number, prove $p$ do not divide $2^p-1$.
Should I prove this using induction? I'm pretty sure there is a better way.