IMO 2022 Shortlist A8
For a positive integer n, an n-sequence is a sequence pa0,...,anq of non-negative integers satisfying the following cond...
Category: Algebra
Problem
For a positive integer n, an n-sequence is a sequence pa0,...,anq of non-negative
integers satisfying the following condition: if i and j are non-negative integers with i j ď n, then ai aj ď n and aaiaj “ aij.
Let fpnq be the number of n-sequences. Prove that there exist positive real numbers c1, c2
and λ such that
c1λn
ă fpnq ă c2λn
for all positive integers n.
(Canada) 4 Oslo, Norway, 6th–16th July 2022