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2020 PUMaC Algebra A8

Source:

January 1, 2022
algebra

Problem Statement

Let ana_n be the number of unordered sets of three distinct bijections f,g,h:{1,2,...,n}→{1,2,...,n}f, g, h : \{1, 2, ..., n\} \to \{1, 2, ..., n\} such that the composition of any two of the bijections equals the third. What is the largest value in the sequence a1,a2,...a_1, a_2, ... which is less than 20212021?
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