IMO Shortlist 1968 problem 25


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2. travnja 2012.
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Let f be a real-valued function defined for all real numbers, such that for some a>0 we have f(x+a)={1\over2}+\sqrt{f(x)-f(x)^2} for all x.
Prove that f is periodic, and give an example of such a non-constant f for a=1.
Izvor: Međunarodna matematička olimpijada, shortlist 1968