关于指数丢番图方程a^(2x)+(3a^2-1)~y=(4a^2-1)~z(英文)

On the Exponential Diophantine Equation a^(2x)+(3a^2-1)~y=(4a^2-1)~z

设a>3是一个整数,应用Bilu,Hanrot和Voutier关于本原素除子的深刻理论以及二次数域类数的一些结果,证明了指数丢番图方程a^(2x)+(3a^2-1)~y=(4a^2-1)~z仅有正整数解x=y=1.

Let a 〉 3 be an integer, we apply a new, deep theorem of Bilu, Hanrot ＆ Voutier and some results on the class number of quadratic field to show that the only positive integer solution of the exponential Diophantine equation a^2x＋（3a^2-1）^y=（4a^2-1）^z is x = y = z = 1.