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arXiv · 1806.02105

On the sums of three generalized polygonal numbers

Hai-Liang Wu·Hao Pan
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Abstract

For each natural number $m\ge 3$, let $P_m(x)$ denote the generalized $m$-gonal number $\frac{(m-2)x^2-(m-4)x}{2}$ with $x\in\mathbb{Z}$. In this paper, with the help of the congruence theta function, we establish conditions on $a$, $b$, $c$ for which the sum $P_a(x)+P_b(y)+P_c(z)$ represents all but finitely many positive integers.

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Hai-Liang Wu, Hao Pan. 2018-06-06. On the sums of three generalized polygonal numbers. https://arxiv.org/abs/1806.02105

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