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Numbers on the Circles Revisited

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

April 5, 2023

number theoryDivisibility

Problem Statement

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