Mixed sums of triangular numbers and certain binary quadratic forms

Kazuhide Matsuda

Mixed sums of triangular numbers and certain binary quadratic forms

Number Theory 2018-03-30 v2

Authors: Kazuhide Matsuda

Abstract

In this paper, we prove that for $d=3,\dots,8$ , every natural number can be written as $t_x+t_y+3t_z+dt_w$ , where $x$ , $y$ , $z$ , and $w$ are nonnegative integers and $t_k=k(k+1)/2$ $(k=0,1,2,\ldots)$ is a triangular number. Furthermore, we study mixed sums of triangular numbers and certain binary quadratic forms.

Keywords

number theory perfect numbers collatz conjecture

Cite

@article{arxiv.1411.5342,
  title  = {Mixed sums of triangular numbers and certain binary quadratic forms},
  author = {Kazuhide Matsuda},
  journal= {arXiv preprint arXiv:1411.5342},
  year   = {2018}
}

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