Two positive integers on the blackboard
Source: Baltic Way 2000 Problem 10
February 13, 2009
functioncombinatorics unsolvedcombinatorics
Problem Statement
Two positive integers are written on the blackboard. Initially, one of them is and the other is smaller than . If the arithmetic mean of the two numbers on the blackboard is an integer, the following operation is allowed: one of the two numbers is erased and replaced by . Prove that this operation cannot be performed more than ten times. Give an example where the operation is performed ten times.