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$f$ is periodic

Source: 6-th Taiwanese Mathematical Olympiad 1997

January 18, 2007
functionalgebra unsolvedalgebra

Problem Statement

Let aa be rational and b,c,db,c,d are real numbers, and let f:R→[−1.1]f: \mathbb{R}\to [-1.1] be a function satisfying f(x+a+b)−f(x+b)=c[x+2a+[x]−2[x+a]−]+df(x+a+b)-f(x+b)=c[x+2a+[x]-2[x+a]-]+d for all xx. Show that ff is periodic.
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