Universal Sums of Triangular Numbers and Squares

Zichen Yang

Universal Sums of Triangular Numbers and Squares

Number Theory 2023-07-06 v1

Authors: Zichen Yang

Abstract

In this paper, we study universal sums of triangular numbers and squares. Specifically, we prove that a sum of triangular numbers and squares is universal if and only if it represents $1,2,3,4,5,6,7,8,10,13,14,15,18,19,20,23,27,28,34,41,47$ , and $48$ .

Keywords

number theory exponential sums

Cite

@article{arxiv.2307.02118,
  title  = {Universal Sums of Triangular Numbers and Squares},
  author = {Zichen Yang},
  journal= {arXiv preprint arXiv:2307.02118},
  year   = {2023}
}

Comments

12 pages

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