## Problem of the Day #409: Sohail’s Function
*May 1, 2012*

*Posted by Saketh in : potd , add a comment*

Sohail is tinkering around with a function $f$. Suddenly, he realizes that his function satisfies the equation $f(x+y) + f(xy) = f(x)f(y) + 1$ for all pairs of integer values $x$ and $y$. Find all possible values of $f(2012)$.