Question 4
An integer $k$ is called olympic if there exist four integers $a, b, c$ and $d$, all coprime to $k$, such that $k$ divides $a^{4}+b^{4}+c^{4}+d^{4}$. Let $n$ be any integer.
Prove that $n^{2}-2$ is olympic.
Prove that $n^{2}-2$ is olympic.