replace a,b with gcd(a, b) and lcm(a, b) in a list of numbers on blackboard
Source: Switzerland - 2004 Swiss MO Final Round p8
December 26, 2022
combinatoricsnumber theoryGCDLCM
Problem Statement
A list of natural numbers is written on a blackboard. The following operation is performed and repeated: choose any two numbers , wipe them out and instead write gcd and lcm. Show that the content of the list no longer changed after a certain point in time.