IMO Shortlist 2008 problem N1


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2. travnja 2012.
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Let n be a positive integer and let p be a prime number. Prove that if a, b, c are integers (not necessarily positive) satisfying the equations
a^n + pb = b^n + pc = c^n + pa
then a = b = c.

Proposed by Angelo Di Pasquale, Australia
Izvor: Međunarodna matematička olimpijada, shortlist 2008