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重庆交通大学学报（自然科学版）

重庆交通大学学报（自然科学版） ›› 1991, Vol. 10 ›› Issue (4): 20-26.

• 大会报告 • 上一篇    下一篇

关于素数模P=3、5的偶次幂同余方程的解

邹兆南   

  1. 基础部
  • 收稿日期:1991-03-28 出版日期:1991-08-26 发布日期:2016-11-09
  • 作者简介:邹兆南,男,51岁,副教授。

On the Solutions of Congruence Equations with Even Number Degree for Prime Number Module P=3,5

Zou Zhaonan   

  1. Department of Basic Courses
  • Received:1991-03-28 Online:1991-08-26 Published:2016-11-09

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摘要： 本文证明了:(1)同余方程x2n+(x+1)2n+…+(x+h)2n≡(x+h+1)2n（mod 3）有解的充分必要条件是:h2,4(mod 9);(2) 同余方程x2n+(x+1)2n+…+(x+h)2n≡(x+h+1)2n （mod 5）有解的充分必要条件是:(i)若n≡0(mod 3),则h2,3,4,8,9,10,14,15,16,18,21,22(mod 25);(ii).若n≡1(mod 2),则h2(mod 5)

关键词: 模, 同余方程, 最小非负剩余, Fermat定理

Abstract: In this paper,we prove that(1) for the Congruence Equation x2n+(x+1)2n+…+(x+h)2n≡(x+h+1)2n (mod 3)there are solutions if and only if h2, 4 (mod 9);(2) for the Congruence Equation x2n+(x+1)+…+(x+h)2n≡(x+h+1)2n (mod 5)there are solutions if and only if(i) if n≡0 (mod 2),then h2, 3,4,8, 9,10,14, 35,16,18,21,22 (mod 25);(ii) if n≡1 (mod 2),then h≠2 (mod 5).

Key words: module, Congruence Equation, least non-negative residue, Fermat's theorem