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Mixed sums of squares and triangular numbers

Zhi-Wei Sun
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Abstract

By means of $q$-series, we prove that any natural number is a sum of an even square and two triangular numbers, and that each positive integer is a sum of a triangular number plus $x^2+y^2$ for some integers $x$ and $y$ with $x\not\equiv y (mod 2)$ or $x=y>0$. The paper also contains some other results and open conjectures on mixed sums of squares and triangular numbers.

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Zhi-Wei Sun. 2007-03-08. Mixed sums of squares and triangular numbers. https://arxiv.org/abs/math/0505128

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