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arXiv · 2411.08398

Arithmetic Polygons and Sums of Consecutive Squares

Jack Anderson·Amy Woodall·Alexandru Zaharescu
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Abstract

We introduce and study arithmetic polygons. We show that these arithmetic polygons are connected to triples of square pyramidal numbers. For every odd $N\geq3$, 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.

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Jack Anderson, Amy Woodall, Alexandru Zaharescu. 2024-11-13. Arithmetic Polygons and Sums of Consecutive Squares. https://arxiv.org/abs/2411.08398

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