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

2015 District Olympiad, 2
Tags: diophantine equation , integer part , number theory
Determine the real numbers $ a,b, $ such that $$ [ax+by]+[bx+ay]=(a+b)\cdot [x+y],\quad\forall x,y\in\mathbb{R} , $$ where $ [t] $ is the greatest integer smaller than $ t. $

2012 District Olympiad, 1
Tags: equation , algebra , fractional part , integer part , floor
Solve in $ \mathbb{R} $ the equation $ [x]^5+\{ x\}^5 =x^5, $ where $ [],\{\} $ are the integer part, respectively, the fractional part.