关于Diophantine方程(ax^3+1)/(ax+1)=f(y)

On The Diophantine Equation (ax^3+1)/(ax+1)=f(y)

设a是大于1的正整数,f(z)是整值函数.本文证明了:方程(ax3+1)/(ax+1)=f(y)没有适合x>1的整数解(x,y).

Let a be a positive integer and let f（z） be an integral valued function. In this paper It is proved that if a〉l, then the equation （αχ^3＋1）/（αχ＋1）=f（y） has no integer solutions （x, y） with x〉l.