2 player game with (n- divisor of n)
Source: 2014 Cuba 1.5
September 20, 2024
combinatoricsnumber theory
Problem Statement
The number 2013 is written on a blackboard. Two players participate, alternating in turns, in the next game. A movement consists in changing the number that is on the board for the difference of this number and one of its divisors. The player who writes a zero loses. Which of the two players can guarantee victory?