MathDB
f(x + 13/42) + f(x) = f(x + 1/6) + f(x + 1/7)

Source: IMO Shortlist 1996, A7

August 9, 2008
functionalgebrapolynomialfunctional equationIMO Shortlistperiodic function

Problem Statement

Let f f be a function from the set of real numbers R \mathbb{R} into itself such for all x∈R, x \in \mathbb{R}, we have ∣f(x)∣≤1 |f(x)| \leq 1 and f \left( x \plus{} \frac{13}{42} \right) \plus{} f(x) \equal{} f \left( x \plus{} \frac{1}{6} \right) \plus{} f \left( x \plus{} \frac{1}{7} \right). Prove that f f is a periodic function (that is, there exists a non-zero real number c c such f(x\plus{}c) \equal{} f(x) for all x∈R x \in \mathbb{R}).
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