moves i sequences, replace a,b by their gcd and lcm
Source: 1999 Swedish Mathematical Competition p6
April 2, 2021
number theoryleast common multiplegreatest common divisorLCMGCD
Problem Statement
is any sequence of at least positive integers. A move is to take any in the sequence such that neither divides the other and replace them by gcd and lcm . Show that only finitely many moves are possible and that the final result is independent of the moves made, except possibly for order.