关于指数丢番图方程x^2+3~m=y^n

On the exponential diophantine equation

利用Bilu,Hanrot和Voutier关于Lucas数本原素除子存在性的深刻结果,证明了指数丢番图方程x2+3m=yn仅有正整数解(x,y,m,n)=(46,13,4,3)适合n>2且gcd(x,y)=1。

By applying the deep theorem of Bilu,Hanrot and Voutier about the existence of primitive divisors of I.ucas numbers,we prove that the exponential diophantine equation x^2＋3^m=y^n has only positive integer solution （x,y,rn ,n） = （46,13,4,3） with n〉2 and gcd= （x,y） =1.