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

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

We apply a new, deep theorem of Bilu, Hanrot ＆ Voutier and some fine results on the representation of the solutions of quadratic Diophantine equations to solve completely the exponential Diophantine equation x^2＋（3a^2-1）^m = （4a^2-1）^n when 3a^2-1 is a prime or a prime power.

应用Bilu,Hanrot和Voutier关于本原素因子的深刻结果以及二次丢番图方程解的表示的一些精细结果,完全解决了指数型丢番图方程x2+(3a2-1)m=(4a2-1)n当3a2-1是奇素数或奇素数幂时的求解问题．