MathDB

8

Part of 2004 Switzerland - Final Round

Problems(1)

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

12/26/2022
A list of natural numbers is written on a blackboard. The following operation is performed and repeated: choose any two numbers a,ba, b, wipe them out and instead write gcd(a,b)(a, b) and lcm(a,b)(a, b). Show that the content of the list no longer changed after a certain point in time.
combinatoricsnumber theoryGCDLCM