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?
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$p$ is prime so it shouldn't be divisible by anything except 1 and $p$. Are you sure you have the statement correct? – Gregory Grant May 05 '15 at 00:44
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You have it backwards, $p$ divides $1 + x^2 + y^2.$ This is a step in the proof that every prime is the sum of four squares. – Will Jagy May 05 '15 at 00:48
