All the species of plants existing in Russia are catalogued (numbered by integers from $2$ to $2000$ ; one after another, without omissions or repetitions). For any pair of species the gcd of their catalogue numbers was calculated and recorded but the catalogue numbers themselves were lost. Is it possible to restore the catalogue numbers from the data in hand?
Problem
Source: Tournament of Towns, Fall 2002, Junior A Level, P2
Tags: number theory, greatest common divisor, combinatorics proposed, combinatorics