Problem

Source: Argentina Cono Sur TST 2024 P2

Tags: number theory



There are $101$ positive integers $a_1, a_2, \ldots, a_{101}$ such that for every index $i$, with $1 \leq i \leq 101$, $a_i+1$ is a multiple of $a_{i+1}$. Find the greatest possible value of the largest of the $101$ numbers.