Mixed sums of triangular numbers and certain binary quadratic forms

Kazuhide Matsuda

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arXiv · 1411.5342

Mixed sums of triangular numbers and certain binary quadratic forms

Kazuhide Matsuda

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Abstract

In this paper, we prove that for $d=3,\dots,8$, every natural number can be written as $t_x+t_y+3t_z+dt_w$, where $x$, $y$, $z$, and $w$ are nonnegative integers and $t_k=k(k+1)/2$ $(k=0,1,2,\ldots)$ is a triangular number. Furthermore, we study mixed sums of triangular numbers and certain binary quadratic forms.

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Kazuhide Matsuda. 2014-11-14. Mixed sums of triangular numbers and certain binary quadratic forms. https://arxiv.org/abs/1411.5342

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