MathDB
number sequence contains every large number

Source: 2021ChinaTST test3 day1 P2

April 13, 2021
number theoryNumber sequenceDivisibility

Problem Statement

Given distinct positive integer a1,a2,…,a2020 a_1,a_2,…,a_{2020} . For n≥2021 n \ge 2021 , ana_n is the smallest number different from a1,a2,…,an−1a_1,a_2,…,a_{n-1} which doesn't divide an−2020...an−2an−1a_{n-2020}...a_{n-2}a_{n-1}. Proof that every number large enough appears in the sequence.
Back to ProblemsView on AoPS