# 2015-9 Sum of squares

Let $$n\ge 1$$ and $$a_0,a_1,a_2,\ldots,a_{n}$$ be non-negative integers. Prove that if $N=\frac{a_0^2+a_1^2+a_2^2+\cdots+a_{n}^2}{1+a_0a_1a_2\cdots a_{n}}$ is an integer, then $$N$$ is the sum of $$n$$ squares of integers.

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