一类方程ax^m-by^n=c无解的判别

The Discrimination of no Solutions on a Kind of Equation ax^m-by^n=c

在[a,b]=1,但[b,c]>1,且[a,c]>1的前提下,根据方程的系数a,b,c所满足的条件,给出一类方程axm-byn=c无正整数解[x,y,m,n]的判别法,证明了该类方程Pillai猜想成立.

On the assumption of[a,b]=1,[b,c]1,and[a,c]1,according to the condition of coefficient a,b,c which are satisfied,we give a method to Discriminate the equation ax^m-by^n=c which has no positive integral solution[x,y,m,n].Then we prove the Pillai conjecture of the equation is right.