IMO Shortlist 1977 problem 10


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2. travnja 2012.
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Let n be a given number greater than 2. We consider the set V_n of all the integers of the form 1 + kn with k = 1, 2, \ldots A number m from V_n is called indecomposable in V_n if there are not two numbers p and q from V_n so that m = pq. Prove that there exist a number r \in V_n that can be expressed as the product of elements indecomposable in V_n in more than one way. (Expressions which differ only in order of the elements of V_n will be considered the same.)
Izvor: Međunarodna matematička olimpijada, shortlist 1977