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arXiv · 1703.03092

Refinements of Lagrange's four-square theorem

Leo Goldmakher·Paul Pollack
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Abstract

A well-known theorem of Lagrange asserts that every nonnegative integer $n$ can be written in the form $a^2+b^2+c^2+d^2$, where $a,b,c,d \in \mathbb{Z}$. We characterize the values assumed by $a+b+c+d$ as we range over all such representations of $n$.

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Leo Goldmakher, Paul Pollack. 2017-03-09. Refinements of Lagrange's four-square theorem. https://arxiv.org/abs/1703.03092

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