Find all the pairs of integers $(x,y)$ for which $(x^2+y)(y^2+x)=(x+1)(y+1).$
Problem
Source: Kyiv mathematical festival 2017
Tags: Kyiv mathematical festival, number theory, Diophantine Equations
Source: Kyiv mathematical festival 2017
Tags: Kyiv mathematical festival, number theory, Diophantine Equations
Find all the pairs of integers $(x,y)$ for which $(x^2+y)(y^2+x)=(x+1)(y+1).$