摘要
本文证明了:(1)同余方程 有解的充分必要条件是: (2) 同余方程 有解的充分必要条件是:
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
h≠2, 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 h≠2, 3,4,8, 9,10,14, 35,16,18,21,22 (mod 25);
(ii) if n=1 (mod 2 ),
then h≠2 (mod 5 ).
出处
《重庆交通学院学报》
1991年第4期20-26,共7页
Journal of Chongqing Jiaotong University
关键词
模
同余方程
最小非负剩余
module, Congruence Equation, least non-negative residue, Fermat's theorem
