This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 27

2011 District Olympiad, 3
Tags: function , algebra , integer part , floor
Let $ f:\mathbb{R}\longrightarrow\mathbb{R} $ be a function with the property that $ (f\circ f) (x) =[x], $ for any real number $ x. $ Show that there exist two distinct real numbers $ a,b $ so that $ |f(a)-f(b)|\ge |a-b|. $ $ [] $ denotes the integer part.

2003 Gheorghe Vranceanu, 1
Tags: algebra , fractional part , integer part
For a real number $ k\ge 2, $ solve the equation $ \frac{\{x\}[x]}{x} =k. $