Arithmetic Polygons and Sums of Consecutive Squares
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910020650663936 |
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| author | Anderson, Jack Woodall, Amy Zaharescu, Alexandru |
| author_facet | Anderson, Jack Woodall, Amy Zaharescu, Alexandru |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08398 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arithmetic Polygons and Sums of Consecutive Squares Anderson, Jack Woodall, Amy Zaharescu, Alexandru Number Theory 11B99 (primary) 11B25 (secondary) 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. |
| title | Arithmetic Polygons and Sums of Consecutive Squares |
| topic | Number Theory 11B99 (primary) 11B25 (secondary) |
| url | https://arxiv.org/abs/2411.08398 |