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5

Part of 2013 China Northern MO

Problems(1)

China Northern Mathematical Olympiad 2013 , Problem 5

Source: China Xian , 27 Jul --3 Aug

8/27/2013
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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