[ [Solving equations in integers $]$ [ Factorization ]

Solve the equation $x y=x+y$ in integers.

#
Express $x$ in terms of $y$. Another possibility is to move all terms to one side.

## Solution

We will express one variable in terms of the other $x=y / y-1=1+1 / y-1$. The last fraction will be an integer only when $y=0$ and $y=2$.

## Answer

$(0,0),(2,2)$.