# AIMO 2015 Q8

**Number Theory**Level 4

Determine the number of non-negative integers \(x\) that satisfy the equation

\[\left \lfloor \dfrac {x}{44} \right \rfloor = \left \lfloor \dfrac {x}{45} \right \rfloor.\]

(Note: if \(r\) is any real number, then \(\lfloor r \rfloor\) denotes the largest integer less than or equal to \(r\).)