IMO 2018 Shortlist C6
Let a and b be distin t positive integers. The following in nite pro ess takes pla e on an initially empty board. piq If...
Category: Combinatorics
Problem
Let a and b be distin t positive integers. The following in nite pro ess takes pla e on an initially empty board. piq If there is at least a pair of equal numbers on the board, we hoose su h a pair and in rease one of its omponents by a and the other by b. piiq If no su h pair exists, we write down two times the number 0. Prove that, no matter how we make the hoi es in piq, operation piiq will be performed only nitely many times. (Serbia)