English

A product rule for triangular numbers

Number Theory 2017-06-28 v2

Abstract

We prove that there are exactly five sequences, including the triangular numbers, that satisfy the product rule T(mn)=T(m)T(n)+T(m1)T(n1)T(mn) = T(m) T(n) + T(m-1) T(n-1) for all m,n1m, n \ge 1.

Cite

@article{arxiv.1606.05398,
  title  = {A product rule for triangular numbers},
  author = {David G. Radcliffe},
  journal= {arXiv preprint arXiv:1606.05398},
  year   = {2017}
}

Comments

7 pages, 3 figures

R2 v1 2026-06-22T14:27:36.462Z