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Similar to chicken mcnugget theorem

Source: Costa Rica National Olympiad, Final Round, Problem 4

November 26, 2011
number theoryrelatively primenumber theory proposed

Problem Statement

Given positive integers a,b,ca,b,c which are pairwise relatively prime, show that 2abc−ab−bc−ac2abc-ab-bc-ac is the biggest number that can't be expressed in the form xbc+yca+zabxbc+yca+zab with x,y,zx,y,z being natural numbers.
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