Two integers on the board
Source: Polish Junior Math Olympiad 2023 Second Stage
May 14, 2023
combinatorics
Problem Statement
Initially, the numbers and are written on the board. A \emph{move} consists of replacing one of the two numbers on the board with their sum. Is it possible to obtain (in a finite numer of moves) a situation in which the two integers written on the board are consecutive? Justify your answer.