Initially, the numbers 1,3,4 are written on a board.
Source: 2024 Mathematics Regional Olympiad of Mexico West P1
October 21, 2024
number theory
Problem Statement
Initially, the numbers are written on a board. We do the following process repeatedly. Consider all of the numbers that can be obtained as the sum of distinct numbers written on the board and that aren't already written, and we write those numbers on the board. We repeat this process, until at a certain step, all of the numbers in that step are greater than . Determine all of the integers that were not written on the board.