关于丢番图方程x^2+y^2=p与x^2+2y^2=p的整数解  

On the Integer Solutions of Diophantine Equations x^2+y^2=p and x^2 + 2y^2=p

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)

机构地区：[1]上海财经大学数学学院,上海200433 [2]上海财经大学浙江学院,浙江金华321013

出　　处：《数学的实践与认识》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)

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).

关 键 词：丢番图方程 p次单位根 同余 简化剩余系 

分 类 号：O156.7[理学—数学]