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arXiv · 2011.01658

Numbers represented by restricted sums of four squares

Guang-Liang Zhou·Yue-Feng She
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Abstract

In this paper, we prove some results of restricted sums of four squares using arithmetic of quaternions in the ring of Lipschitz integers. For example, we show that every nonnegative integer $n$ can be written as $x^{2}+y^{2}+z^{2}+t^{2}$ where $x,y,z,t$ are integers and $x+y+2z+2t$ is a square or a cube.

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Guang-Liang Zhou, Yue-Feng She. 2020-11-03. Numbers represented by restricted sums of four squares. https://arxiv.org/abs/2011.01658

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