一类偶次幂同余方程的解  

The Solution of the Congruence Equation with Even Exponents

作　　者：陈心怡 罗家贵 CHEN Xinyi;LUO Jiagui(School of Mathematic and Information,China West Normal University,Nanchong,Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《内江师范学院学报》2020年第8期32-35,共4页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目(11871058);四川省教育厅重大培育项目(16ZA0173)。

摘　　要：连续整数偶次幂之和关于模pr的同余方程的整数解问题是一个古老而至今尚未完全解决的数论问题.利用同余理论和分类讨论的思想,得到了该同余方程在φ(pr)|2n时有解的充分必要条件,并且在有解的情况下,给出了方程全部的整数解.The integer solution problem of the congruence equation for the sum of even exponents of continuous integers with respect to modulo p r is a centuries old theory problem which hasn’t yet been solved completely up to now,is put under examination.By useing of the congruent theory and the classified discussion,the necessary and sufficient conditions under which whenφp r divides 2n,the congruence equation has solutions,are obtained.Under the condition of there existing solutions to the congruence equation,all the positive integer solutions of the congruence equation are put forth.

关 键 词：连续整数 高次同余方程 整数解 完全剩余 

分 类 号：O156.1[理学—数学]