Factorials and Legendre's three-square theorem: II

Rob Burns

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arXiv · 2203.16469

Factorials and Legendre's three-square theorem: II

Rob Burns

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Abstract

Let $\bar{S}$ denote the set of integers $n$ such that $n!$ cannot be written as a sum of three squares. Let $\bar{S}(n)$ denote $\bar{S} \cap [1, n]$. We establish an exact formula for $\bar{S}(2^k)$ and show that $\bar{S}(n) = 1/8*n + \mathcal{O}(\sqrt{n})$. We also list the lengths of gaps appearing in $\bar{S}$. We make use of the software package Walnut to establish these results.

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BibTeX RIS

Rob Burns. 2022-03-30. Factorials and Legendre's three-square theorem: II. https://arxiv.org/abs/2203.16469

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