Weighted sums of generalized polygonal numbers with coefficients 1 or 2

Daejun Kim

Weighted sums of generalized polygonal numbers with coefficients 1 or 2

Number Theory 2022-01-11 v2

Authors: Daejun Kim

Abstract

In this article, we consider weighted sums of generalized polygonal numbers with coefficients $1$ or $2$ . We show that for any $m\ge10$ , those weighted sums of generalized $m$ -gonal numbers represent every non-negative integers if they only represent $1$ , $m-4$ , and $m-2$ . Furthermore, we study representations of sums of four generalized polygonal numbers with coefficients $1$ or $2$ .

Keywords

generalized polygonal numbers weighted sums non-negative integers representations coefficients

Cite

@article{arxiv.2006.04490,
  title  = {Weighted sums of generalized polygonal numbers with coefficients 1 or 2},
  author = {Daejun Kim},
  journal= {arXiv preprint arXiv:2006.04490},
  year   = {2022}
}

Comments

13 pages

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