摘要
本文证明了,同余方程 x^(2n)+(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h3,4(mod 7); (3)若n≡2(mod 3),则h4(mod 7)。
In this paper, we prove that for the congruence equation
x2n+(x+l)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).
出处
《重庆交通学院学报》
1992年第1期45-52,共8页
Journal of Chongqing Jiaotong University
关键词
最小非负剩余
同余方程
数论
module, minimal nonnegative residue, congruence equation, Fermat theorem
