English

Arithmetic Polygons and Sums of Consecutive Squares

Number Theory 2026-02-16 v2

Abstract

We introduce and study arithmetic polygons. We show that these arithmetic polygons are connected to triples of square pyramidal numbers. For every odd N3N\geq3, we prove that there is at least one arithmetic polygon with NN sides. We also show that there are infinitely many arithmetic polygons with an even number of sides.

Keywords

Cite

@article{arxiv.2411.08398,
  title  = {Arithmetic Polygons and Sums of Consecutive Squares},
  author = {Jack Anderson and Amy Woodall and Alexandru Zaharescu},
  journal= {arXiv preprint arXiv:2411.08398},
  year   = {2026}
}

Comments

22 pages, 6 figures, 2 tables; typos corrected

R2 v1 2026-06-28T19:58:02.126Z