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Floor functions in f(x)

Source: Saudi Arabia IMO TST Day III Problem 2

July 22, 2014
functionfloor functioninductionlogarithmsalgebra unsolvedalgebra

Problem Statement

Determine all functions f:[0,∞)→Rf:[0,\infty)\rightarrow\mathbb{R} such that f(0)=0f(0)=0 and f(x)=1+5f\left(\left\lfloor{\frac{x}{2}\right\rfloor}\right)-6f\left(\left\lfloor{\frac{x}{4}\right\rfloor}\right) for all x>0x>0.
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