Abstract: In this paper, wc prove that fur the diophantine congruence equation x2n+(x+1)2n+…+(x+h)2n≡(x+ h + 1)2n(mod 17)there are integer solutions if and only if(1)when n≡4(mod 8),(mod 17):(2)when n≡5 (mod 8)(mod 17):(3)when n≡6(mod 8)(mod 17);(4)when n≡7(mod 8)(mod 17)

Key words: module, minimal non-negative residue:congruence pouation, Fermat’s theorem

摘要： 本文证明了:不定同余方程z2n+(x+1) 2n+…+(x+h)2n≡(x+h+1)2n (mod 17)有整数解的充分必要条件是(１)若ｎ≡４(ｍｏｄ８)，则h?14(mod 17)?(2)若ｎ≡5(mod8)，则h?18,12,13(mod 17)(3)若ｎ≡6(mod8)，则h?3,4,9,10,14(mod 17)(４)若ｎ≡7(mod8)，则h?5,6(mod 17)

关键词: 模, 同余方程, 最小非负剩余, Fermat定理