Problem

Source: Iran TST 2012-Second exam-1st day-P1

Tags: induction, graph theory, greatest common divisor, combinatorics proposed, combinatorics



Is it possible to put \binom{n}{2} consecutive natural numbers on the edges of a complete graph with n vertices in a way that for every path (or cycle) of length 3 where the numbers a,b and c are written on its edges (edge b is between edges c and a), b is divisible by the greatest common divisor of the numbers a and c? Proposed by Morteza Saghafian