Almost universal ternary sums of polygonal numbers

Anna Haensch; Ben Kane

Almost universal ternary sums of polygonal numbers

Number Theory 2017-10-30 v4

Authors: Anna Haensch , Ben Kane

Abstract

For a natural number $m$ , generalized $m$ -gonal numbers are those numbers of the form $p_m(x)=\frac{(m-2)x^2-(m-4)x}{2}$ with $x\in \mathbb Z$ . In this paper we establish conditions on $m$ for which the ternary sum $p_m(x)+p_m(y)+p_m(z)$ is almost universal.

Keywords

polygonal numbers ternary sums almost universal generalized m-gonal numbers number theory quadratic forms

Cite

@article{arxiv.1607.06573,
  title  = {Almost universal ternary sums of polygonal numbers},
  author = {Anna Haensch and Ben Kane},
  journal= {arXiv preprint arXiv:1607.06573},
  year   = {2017}
}

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