MathDB

How to Play a Infinite Writing-Number Game

Source: 2018 China Team Selection Test 2 Problem 3

January 8, 2018

combinatoricsTSTChina TST

Problem Statement

Two positive integers

p,q \in \mathbf{Z}^{+}

are given. There is a blackboard with

n

positive integers written on it. A operation is to choose two same number

a,a

written on the blackboard, and replace them with

a+p,a+q

. Determine the smallest

n

so that such operation can go on infinitely.