Problem

Source: Ukrainian Mathematical Olympiad 2023. Day 2, Problem 10.7

Tags: number theory



You are given $n \ge 2$ distinct positive integers. For every pair $a<b$ of them, Vlada writes on the board the largest power of $2$ that divides $b-a$. At most how many distinct powers of $2$ could Vlada have written? Proposed by Oleksiy Masalitin