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Sum of floor function.

Source: Rioplatense problem 4 2012.

October 7, 2014
floor functionalgebra proposedalgebra

Problem Statement

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