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Numbers represented by restricted sums of four squares (2011.01658v2)
Published 3 Nov 2020 in math.NT
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.