2023 Polish Junior Math Olympiad Round 1 P4
Source:
May 21, 2023
combinatorics
Problem Statement
Each of the natural numbers from to is colored either red or blue, with each color being used at least once. It turns out that:
– every red number is a sum of two distinct blue numbers; and
– every blue number is a difference between two red numbers.
Determine the smallest possible value of for which such a coloring exists.