摘要
利用p次单位根e^2πi/p作为原始材料,通过不同层次的组合,当p≡1(mod 4)时,给出了方程x^2+y^2=p的整数解.在此基础上,当p≡1(mod 8)时,进一步给出了x^2+2y^2=p的整数解.
In this paper,p-th order unity is used as the starting point,the integer solutions of equation x^2+y^2=p are given when p≡1(mod 4).On this basis,the integer solutions of equation x^2+2y^2=p are given when p≡1(mod 8).
作者
汤健儿
何其祥
TANG Jian-er;HE Qi-xiang(School of Mathematics,Shanghai University of Finance and Economics,Shanghai 200433,China;Zhejiang College,Shanghai University of Finance and Economics,Jinhua 321013,China)
出处
《数学的实践与认识》
北大核心
2019年第13期230-238,共9页
Mathematics in Practice and Theory
基金
国家自然科学基金(11671097)
关键词
丢番图方程
p次单位根
同余
简化剩余系
Diophantine equation
p-th order unity
congruence
reduced residue system
