IMO Shortlist 1975 problem 11


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2. travnja 2012.
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Let a_{1}, \ldots, a_{n} be an infinite sequence of strictly positive integers, so that a_{k} < a_{k+1} for any k. Prove that there exists an infinity of terms a_m, which can be written like a_m = x \cdot a_p + y \cdot a_q with x,y strictly positive integers and p \neq q.
Izvor: Međunarodna matematička olimpijada, shortlist 1975