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Generalization of ISL 2008 problem

Source: Benelux 2009

January 29, 2011
IMO Shortlistnumber theory proposednumber theory

Problem Statement

Let nn be a positive integer and let kk be an odd positive integer. Moreover, let a,ba,b and cc be integers (not necessarily positive) satisfying the equations an+kb=bn+kc=cn+kaa^n+kb=b^n+kc=c^n+ka Prove that a=b=ca=b=c.
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