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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） ›› 1992, Vol. 11 ›› Issue (1): 45-52.

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一类偶次幂同余方程的解

邹兆南   

  1. 基础部
  • 收稿日期:1991-05-01 出版日期:1992-02-22 发布日期:2016-11-08
  • 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 Modulo p=7

Zou Zhaonan   

  1. Department of Basic Courses
  • Received:1991-05-01 Online:1992-02-22 Published:2016-11-08

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摘要： 本文证明了,同余方程x2n+(x+1)2n+…+(x+h)2n≡(x+h+1)2n(mod 7)有解的充分必要条件是:(1)若n≡0(mod 3),则h≡0,1,7,8,9,15,16,17,23,24,25;31,32,33,39,41,42,47,48(mod 49);(2)若n≡1(mod 3),则h≢3,4(mod 7);(3)若n≡2(mod 3),则h≢4(mod 7)。

关键词: 模, 最小非负剩余, 同余方程, Fermat定理

Abstract: In this paper,we prove that for the congruence equation x2n+(x+1)2n+…+(x+h)2n≡(x+h+1)2n(mod 7) there are solutions if and only if (1) when n≡0(mod 3),then h≡0,1,7,8,9,15,16,17,23,24,25;31,32,33,39,41,42,47,48(mod 49);(2) when n≡1(mod 3),then h≢3,4(mod 7);(3) when n≡2(mod 3),then h≢4(mod 7).

Key words: module, minimal nonnegative residue, congruence equation, Fermat theorem