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Is there a positive integer $N$ such that the equation $x^2 + y^2 = N$ has at least $2005$ solutions in non-negative integers $x$ and $y$? If so, prove it. If not, prove it!

asdf
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    http://math.stackexchange.com/questions/17496/number-of-integer-solutions-of-x2-y2-k – Yiyuan Lee Jul 18 '14 at 00:43
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    However, that link is useful when you are given $k$ (or $N$ in this case). Here you are given the number of solutions and asked to find if $N$ exists (you don't necessarily have to find it). – asdf Jul 18 '14 at 00:56

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