# Divisibility properties in a sequence

**Number Theory**Level 5

Suppose \(n_1,n_2,...,n_{10}\) are 10 distinct positive integers, all greater than \(1.\) What is the largest possible number of ordered pairs \((i,j)\) such that \(2^{n_i}-1\) is a multiple of \(n_j?\)

**Details and assumptions**

You may use the fact that \( ^{10}P_2 = 90 \).