论文标题
由四个正方形的限制总和表示的数字
Numbers represented by restricted sums of four squares
论文作者
论文摘要
在本文中，我们证明了使用Lipschitz整数环中四个正方形的限制总和的一些结果。例如，我们表明，每个非负整数$ n $都可以写为$ x^{2}+y^{2}+z^{2}+t}+t^{2} $其中$ x，y，y，z，t $是整数，$ x+x+x+y+y+y+2z+2t $ as Square或a Square或a cube。
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.
