Find all integers \( n \) such that \( n^4 + n^3 + n^2 + n + 1 \) is a perfect square.

Suppose that \( x, y, z \) are positive integers satisfying
\[
0 \leq x^2 + y^2 – xyz \leq z+1.
\]
Prove that \( x^2 + y^2 – xyz \) is a perfect square.