Question 65
Let $p$ be a prime. Determine all positive integers $n$ for which the following condition is satisfied for all the integers $x$:
Condition: If $x^n - 1$ is divisible by $p$, then it is also divisible by $p^2$.
Condition: If $x^n - 1$ is divisible by $p$, then it is also divisible by $p^2$.