IMO 2023 Shortlist A7
Let N be a positive integer. Prove that there exist three permutations a1,a2,...,aN; b1,b2,...,bN; and c1,c2,...,cN of 1...
Category: Algebra
Problem
Let N be a positive integer. Prove that there exist three permutations a1,a2,...,aN;
b1,b2,...,bN; and c1,c2,...,cN of 1,2,...,N such that
?
ak a bk
?
ck ´ 2
?
N ă 2023
for every k “ 1,2,...,N.
(China) Shortlisted problems 5