Let $n$ be a positive integer and $p$ be a prime number such that $np+1$ is a perfect square. Prove that $n+1$ can be written as the sum of $p$ perfect squares.
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Tags: number theory proposed, number theory
Let $n$ be a positive integer and $p$ be a prime number such that $np+1$ is a perfect square. Prove that $n+1$ can be written as the sum of $p$ perfect squares.