IMO Shortlist 1986 problem 4


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2. travnja 2012.
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Provided the equation xyz = p^n(x + y + z) where p \geq 3 is a prime and n \in \mathbb{N}. Prove that the equation has at least 3n + 3 different solutions (x,y,z) with natural numbers x,y,z and x < y < z. Prove the same for p > 3 being an odd integer.
Izvor: Međunarodna matematička olimpijada, shortlist 1986