show $p$ is divisible by $(x^2 +y^2 +1)$ Show that, for any prime $p$, there are integers $x$, and $y$ such that $p$ is divisible by $(x^2+y^2+1)$    Can you show me what to start with? do I prove $p$ is divisible by $x^2$ and $y^2$ separately?

Take $x=y=0$, then $x^2+y^2+1=1$, then $p$ is divisible by $x^2+y^2+1=1$.
