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IMO ShortList 2008, Number Theory problem 1

Source: IMO ShortList 2008, Number Theory problem 1

July 9, 2009
algebranumber theoryIMO Shortlistequation

Problem Statement

Let nn be a positive integer and let pp be a prime number. Prove that if aa, bb, cc are integers (not necessarily positive) satisfying the equations an+pb=bn+pc=cn+pa a^n + pb = b^n + pc = c^n + pa then a=b=ca = b = c.
Proposed by Angelo Di Pasquale, Australia
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