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Divisibility on 101 integers

Source: Argentina Cono Sur TST 2024 P2

August 9, 2024
number theory

Problem Statement

There are 101101 positive integers a1,a2,…,a101a_1, a_2, \ldots, a_{101} such that for every index ii, with 1≤i≤1011 \leq i \leq 101, ai+1a_i+1 is a multiple of ai+1a_{i+1}. Find the greatest possible value of the largest of the 101101 numbers.
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