IMO Shortlist 1983 problem 18


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2. travnja 2012.
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Let a,b and c be positive integers, no two of which have a common divisor greater than 1. Show that 2abc-ab-bc-ca is the largest integer which cannot be expressed in the form xbc+yca+zab, where x,y,z are non-negative integers.
Izvor: Međunarodna matematička olimpijada, shortlist 1983