# IMO 2007 Shortlist

Number Theory Level 5

For natural numbers $$x$$ and $$y$$, let $$\gcd(x, y)$$ denote the greatest common divisor of $$x$$ and $$y$$. How many pairs of natural numbers $$x$$ and $$y$$ such that they satisfy the equation below?

$xy = x + y + \gcd (x, y)$

×