AIMO 2015 Q8

Determine the number of non-negative integers xx that satisfy the equation

x44=x45.\left \lfloor \dfrac {x}{44} \right \rfloor = \left \lfloor \dfrac {x}{45} \right \rfloor.

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

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