AIMO 2015 Q8

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 \(r\).)

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