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Show that f is a periodic function

Source: Iran Pre-Preparation Course Examination 1997, E1, P1

October 17, 2005

functionalgebra proposedalgebra

Problem Statement

Let

f: \mathbb R \to\mathbb R

be a function such that

|f(x)| \leq 1

for all

x \in \mathbb R

and f \left( x + \frac{13}{42} \right) + f(x) = f \left( x + \frac 17 \right) + f \left( x + \frac 16 \right), \forall x \in \mathbb R. Show that

f

is a periodic function.