关于Diophantine方程xn+1=2y2

ON THE DIOPHANTINE EQUATION x^n+1=2y^2

运用Gel'fond-Baker方法证明了:如果(n,x,y)是方程xn+1=2y2适合n>2以及x>1的正整数解,则n必为小于56000的无平方因子正奇数.

In this paper, using the Gelfond - Baker method, we prove that if （n, x, y） is a positive integer solution of the equation x^n ＋ 1 = 2y^2 , n 〉 2, x 〉 1, then n 〈 56000 and n is an odd integer with square free.