Problem

Source: Rioplatense problem 4 2012.

Tags: floor function, algebra proposed, algebra



Find all real numbers $x$, such that: a) $\lfloor x \rfloor + \lfloor 2x \rfloor +...+ \lfloor 2012x \rfloor = 2013$ b) $\lfloor x \rfloor + \lfloor 2x \rfloor +...+ \lfloor 2013x \rfloor = 2014$