Problem

Source: Ukrainian Mathematical Olympiad 2023. Day 1, Problem 9.2

Tags: number theory, Divisibility



Positive integers $a_1, a_2, \ldots, a_{101}$ are such that $a_i+1$ is divisible by $a_{i+1}$ for all $1 \le i \le 101$, where $a_{102} = a_1$. What is the largest possible value of $\max(a_1, a_2, \ldots, a_{101})$? Proposed by Oleksiy Masalitin