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sum of numbers with maxized gcd

Source: flanders '98

August 30, 2004
number theorygreatest common divisorinequalities

Problem Statement

Prove there exist positive integers a,b,c for which a+b+c=1998a+b+c=1998, the gcd is maximized, and 0<a<b≤c<2a0<a<b\leq c<2a. Find those numbers. Are they unique?
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