MathDB

Let

n

be a positive integer. The numbers

1,2,3,\dots, 4n

are written in a board. Olive wants to make some "couples" of numbers, such that the product of the numbers in each couple is a perfect square. Each number is in, at most, one couple and the two numbers in each couple are distincts. Determine, for each positive integer

n

, the maximum number of couples that Olive can write.

Problem Statement