In this paper,we prove that(1) for the Congruence Equation x
2n+(x+1)
2n+…+(x+h)
2n≡(x+h+1)
2n (mod 3)there are solutions if and only if h
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2, 4 (mod 9);(2) for the Congruence Equation x
2n+(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
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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).