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.
2026-04-06 20:59:19.1775509159
Finite sum of a floor function
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