MathDB
Denominators are powers of 3

Source: South Africa 1999

September 30, 2005
functionnumber theory unsolvednumber theory

Problem Statement

Let SS be the set of all rational numbers whose denominators are powers of 3. Let aa, bb and cc be given non-zero real numbers. Determine all real-valued functions ff that are defined for x∈Sx \in S, satisfy f(x)=af(3x)+bf(3x−1)+cf(3x−2) if 0≤x≤1, f(x) = af(3x) + bf(3x - 1) + cf(3x - 2) \textrm{ if }0 \leq x \leq 1, and are zero elsewhere.
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