If we are given $x,y$ both integers where $x>y>1$ for the expression $$(x^{\frac{a}{b}} - y)\cdot y^{b}$$ Is there any way to find integer values for a,b in which this expression is minimal and positive. I'm not sure if it is possible or if the answer can lie at infinity. So any feedback would be helpful.
Edit: x,y,a,b are all positive integers