关于不定方程(a^nx^m±1)/(a^nx±1)=y^n

On the Diophantine Equation (a^nx^m±1)/(a^nx±1)=y^n

证明了方程 (anxm± 1) /(anx± 1) =yn没有x是一个n次完全幂的整数解 (a ,x ,y ,m ,n) ,推广了乐茂华的结论 :(xm- 1) /(x - 1) =yn没有x是一个n次完全幂的整数解 (x ,y,m ,n) .

In this paper,we have proved that the diophantine equation (a nx m±1)/(a nx±1)=y n has no solutions (a,x,y,m,n),which make x an n-th perfect power. So we have generalized the result by Le Maohua that the diophantine equation (x m-1)/(x-1)=y n has no solutions (x,y,m,n) to make x an n-th perfect power.