IMO 2021 Shortlist N2

Let n ě100 be an integer. The numbers n,n 1,...,2n are written on n 1 cards, one number per card. The cards are shuffled...

IMO 2021 Shortlist N2

Category: Number Theory

Problem

Let n ě100 be an integer. The numbers n,n 1,...,2n are written on n 1 cards, one number per card. The cards are shuffled and divided into two piles. Prove that one of the piles contains two cards such that the sum of their numbers is a perfect square.