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arXiv · 1802.08374

Universal sums of $m$-gonal numbers

Ben Kane·Jingbo Liu
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Abstract

In this paper we study universal quadratic polynomials which arise as sums of polygonal numbers. Specifically, we determine an asymptotic upper bound (as a function of $m$) on the size of the set $S_m\subset\mathbb{N}$ such that if a sum of $m$-gonal numbers represents $S_m$, then it represents $\mathbb{N}$.

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Ben Kane, Jingbo Liu. 2018-02-23. Universal sums of $m$-gonal numbers. https://arxiv.org/abs/1802.08374

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