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Powers of Two and Differences

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

April 5, 2023

number theory

Problem Statement

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