NUMBERS REPRESENTED BY RESTRICTED SUMS OF FOUR SQUARES

被引：1
|
作者：
She, Yue-Feng [1 ]
Zhou, Guang-Liang [2 ]
机构：
[1] Nanjing Forestry Univ, Dept Appl Math, Nanjing, Peoples R China
[2] Tongji Univ, Sch Math Sci, Shanghai, Peoples R China
来源：
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2024年 / 54卷 / 04期
基金：
中国国家自然科学基金;
关键词：
quaternions; Lipschitz integers; sums of squares;
D O I：
10.1216/rmj.2024.54.1141
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove some results of restricted sums of four squares using arithmetic of quaternions in the ring of Lipschitz integers. In particular, 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 + 3y y + 3z z is a power of 2.
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页码：1141 / 1147
页数：7
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