This question was asked in my number theory quiz, but I am unable to solve it.
Let $a, b, n$ be positive integers such that $n$ divides $a^n -b^n $. Prove that $n$ also divides $ \dfrac{a^n -b^n}{a-b}$.
I started by writing $ a^n -b^n = (a-b) ( a^{n-1} +... + b^{n-1} ) \equiv 0 \mod n $ . But I don't understand what can I do from it and which result should be used.
Can you please help.
Thank you!!
