MathNet 2023-part-07 — 187 problems (EN–VI) Question 10

You are given $n \ge 2$ distinct positive integers. For each pair $a \lt b$ of these numbers, consider the difference $b - a$. For each of these differences, Vlada writes down the maximum power of two by which this difference is divisible. What is the largest possible number of distinct numbers that Vlada could write?
(Oleksii Masalitin)