Arithmetic Polygons and Sums of Consecutive Squares

Abstract

We introduce and study arithmetic polygons. We show that these arithmetic polygons are connected to triples of square pyramidal numbers. For every odd $N\ge 3$, we prove that there is at least one arithmetic polygon with $N$ sides. We also show that there are infinitely many arithmetic polygons with an even number of sides.

22 pages, 6 figures, 2 tables; typos corrected