Problem 3 - Greatest Common Divisor
Source: 2020 Austrian National Competition for Advanced Students, Part 1 problem 3
June 6, 2020
combinatoricsgreatest common divisorAustria
Problem Statement
On a blackboard there are three positive integers. In each step the three numbers on the board are denoted as such that , then gets replaced by . The game ends if there is no way to denote the numbers such that .Prove that the game always ends and that the last three numbers on the blackboard only depend on the starting numbers.(Theresia Eisenkölbl)