MathDB

1

Part of 1998 Flanders Math Olympiad

Problems(1)

sum of numbers with maxized gcd

Source: flanders '98

8/30/2004
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?
number theorygreatest common divisorinequalities