IMO Shortlist 2005 problem N3


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Dodao/la: arhiva
2. travnja 2012.
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Let a, b, c, d, e, f be positive integers and let S = a+b+c+d+e+f.
Suppose that the number S divides abc+def and ab+bc+ca-de-ef-df. Prove that S is composite.
Izvor: Međunarodna matematička olimpijada, shortlist 2005