MathDB
sort of functional equation

Source: flanders '89

September 27, 2005
induction

Problem Statement

Let DD be the set of positive reals different from 11 and let nn be a positive integer. If for f:D→Rf: D\rightarrow \mathbb{R} we have xnf(x)=f(x2)x^n f(x)=f(x^2), and if f(x)=xnf(x)=x^n for 0<x<119890<x<\frac{1}{1989} and for x>1989x>1989, then prove that f(x)=xnf(x)=x^n for all x∈Dx \in D.
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