用e^(2πi/p)表示丢番图方程x^2＋27y^2=4p的整数解  

Use e^(2πi/p) to present the integer solution of Diophantine equation x^2+27y^2=4p

作　　者：汤健儿[1] 汤卓立 

机构地区：[1]上海财经大学应用数学系,上海200433 [2]Management Pathway, Winchester School of Art, Winchester, UK, S023 8DL

出　　处：《四川大学学报（自然科学版）》2013年第4期689-692,共4页Journal of Sichuan University(Natural Science Edition)

摘　　要：把素数表示为一些正整数平方和的问题是数论中基本问题之一.历史上如Fermat,Euler,Gauss等著名数学家都曾深入研究过.本文对于任何一个p≡1(mod 3)类型素数,从p次单位根e2πi/p开始,通过不同层次的组合推导出一组正整数A,B,使得4p=A2+27B2,进而把p表示成x2+3y2.Fermat, Euler, Gauss, famous mathematicians in the history, spend years on research of the basic issue of number theory： how to present integer number quadratic sum with the form of prime num- ber. This artic is design to solve this problem. To any prime number p = 1（rood 3）, this article tries to conclude a set of integer number, starting from （pth） unit root to acquire 4p = Az -b 27Bz and then, present x2 -b 3y2 by using p.

关 键 词：p≡1(mod3)类型素数 p次单位根 同余 缩剩余系 

分 类 号：O156[理学—数学]