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On the Solutions of Congruence Equations with Even Number Degree for Prime Number Modulo p=7
Zou Zhaonan
1992, 11(1):
45-52.
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).
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