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China Northern Mathematical Olympiad 2013 , Problem 5

Source: China Xian , 27 Jul --3 Aug

August 27, 2013
algebra proposedalgebrafloor functionSolve equation

Problem Statement

Find all non-integers xx such that x+13x=[x]+13[x].x+\frac{13}{x}=[x]+\frac{13}{[x]} . where[x][x] mean the greatest integer nn , where n≤x.n\leq x.
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