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Another question from an old MPhil paper: Is there a way to compute an expression for $$\sum_{y=1}^{\lfloor0.5(\sqrt{2x-1}-1)\rfloor}\lfloor0.5(\sqrt{x-y^2}-y-1)\rfloor$$ Other than brute force case-by-case sum I am unable to come up with an expression. Any help will be greatly appreciated.

Wilbur
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  • I'm not sure this matters, but do we know if $x$ is an integer? – saulspatz May 31 '19 at 11:52
  • Let us assume for the moment that both $x$ and $y$ are positive integers. If this special case could be solved, so can the original, I think. – Wilbur May 31 '19 at 12:24

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