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An arithmetic progression

Source: India National Olympiad 2002, Problem 5

October 10, 2005
arithmetic sequencealgebra unsolvedalgebra

Problem Statement

Do there exist distinct positive integers aa, bb, cc such that aa, bb, cc, −a+b+c-a+b+c, a−b+ca-b+c, a+b−ca+b-c, a+b+ca+b+c form an arithmetic progression (in some order).
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