VWO 1998 Problem 1

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

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.