Question 25
Let $a$, $b$, $c$, $n$ be integers, with $n \geq 2$. Let $p$ be a prime number that divides $a^{2}+ab+b^{2}$ and $a^{n}+b^{n}+c^{n}$, but does not divide $a+b+c$.
Prove that $n$ and $p-1$ are not coprime.
Prove that $n$ and $p-1$ are not coprime.