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Prove that there exists a positive integer N such that there are at least 2005 ordered pairs (x, y) of non-negative integers x and y, satisfying x^2+y^2=N.

 Jun 12, 2020
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You can use Schinzel's Theorem: https://mathworld.wolfram.com/SchinzelsTheorem.html

 Jun 12, 2020

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