关于Diophantine方程x^3-2^(3n)=Dy^2

On the Diophantine Equation x^3-2^(3n)=Dy^2

设D是不能被6k+1之形素数整除的无平方因子正奇数时,论文证明了:如果D≡1,3(mod8)或D有适合p≡5(mod12)的素因数p,则方程2332Dyxn=-没有适合n>1的正整数解(x,y,n).

Let D be a positive odd integer with square free, and D is not divisible by primes of the form 6k+1. In this paper we prove that if either D≡1,3 (mod 8) or D has a prime divisor p with p≡5 (mod 12), then the equation 2332Dyxn=-has no positive integer solutions (x,y,n) with n>1.