Question 152
Let $n \ge 2$ be a positive integer. Prove that the following assertions are equivalent:
a) for all integer $x$ coprime with $n$ the congruence $x^6 \equiv 1 \pmod{n}$ holds;
b) $n$ divides 504.
a) for all integer $x$ coprime with $n$ the congruence $x^6 \equiv 1 \pmod{n}$ holds;
b) $n$ divides 504.