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 , we prove that there is at least one arithmetic polygon with 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