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Functional Equation

Source: 2018 Korea Winter Program Practice Test 1 #1

January 7, 2018
functional equationfunctionfloor functionalgebra

Problem Statement

Find all functions f:R→Rf : \mathbb{R} \rightarrow \mathbb{R} satisfying the following conditions : 1) f(x+y)−f(x)−f(y)∈{0,1}f(x+y)-f(x)-f(y) \in \{0,1\} for all x,y∈Rx,y \in \mathbb{R} 2) ⌊f(x)⌋=⌊x⌋\lfloor f(x) \rfloor = \lfloor x \rfloor for all real xx.
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