Integral solutions to expression given below.

Question

Given expression $xy=2^23^45^7(x+y)$ What are its integral solutions? I tried to solve it by converting it to $\frac{1}{2^2}\frac{1}{3^4}\frac{1}{5^7}=\frac{1}{x}+\frac{1}{y}$ But thereafter it got a li'l messy. I'd appreciate some help.

Answer 1

HINT: Suppose $xy=q(x+y)$ then $xy-qx-qy+q^2=q^2=(x-q)(y-q)$

That should be enough to enable you to identify the possible values.