一族带参数指数型不定方程的总解数

Total Number of Solutions of a Family of Exponential Diophantine Equations with a Parameter

证明了以m为参数时,如果固定m的类型,l取自特定的集合时,不定方程的集合{m=l|l∈lL}的总解数有限,并且提出了关于解数上界的若干猜想。

In this paper we prove that total number of solutions of diophantine equations {m=l｜l∈lL} is finite if the type of the parameter m and the set L are fixed, and bring forward some conjectures on the upper bound of number of solutions.