IMO Shortlist 1996 problem A7


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2. travnja 2012.
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Let f be a function from the set of real numbers \mathbb{R} into itself such for all x \in \mathbb{R}, we have |f(x)| \leq 1 and

f \left( x + \frac{13}{42} \right) + f(x) = f \left( x + \frac{1}{6} \right) + f \left( x + \frac{1}{7} \right).

Prove that f is a periodic function (that is, there exists a non-zero real number c such f(x+c) = f(x) for all x \in \mathbb{R}).
Izvor: Međunarodna matematička olimpijada, shortlist 1996