Question 136
Given $a_1, a_2, ..., a_{2009}$ different natural numbers such that if two of any three numbers are not relatively prime, then one of the two numbers is not relatively prime to the third. If there do not exist 50 numbers that are relatively prime pairwise, then prove that there exist 40 numbers such that are not relatively prime pairwise.
(proposed by B. Bayasgalan)
(proposed by B. Bayasgalan)