关于Ramanujan-Nagell方程D_1x^2+2~mD_2=p^n

On the generalized Ramanujan-Nagell equation D1x2+ 2mD2 = Pn

设P是奇素数,又设D1,D2是适合D1>1,D2>1,ged(D1,D2)=1,D1 D2≠0,(mod p)的正奇数.证叫了方程D1x2+2mD2=pn至多有2组正整数解(x,m,n).

Let p be an odd prime,and let D1, D2 be odd integers such that D1> 1, D2 > 1 ,gcd(D1, D2) = 1, D1,D2 0 (mod p) . In this paper we prove that the equation D1x2 + 2mD2=Pn has at most two positive integer solutions ( x , m , n ) .