Product of pairs is a perfect square
Source: 2024 Azerbaijan BMO TST
July 18, 2024
combinatoricsAZE BMO TSTTST
Problem Statement
Let be a positive integer. Using the integers from to inclusive, pairs are to be formed such that the product of the numbers in each pair is a perfect square. Each number can be part of at most one pair, and the two numbers in each pair must be different. Determine, for each , the maximum number of pairs that can be formed.