Source: Nick's Mathematical Puzzles
Problem:Let n be a positive integer, and let \(S_n = {n^2 + 1, n^2 + 2, ... , (n + 1)^2}\). Find, in terms of n, the cardinality of the set of pairwise products of distinct elements of \(S_n\)
For example, \(S_2 = {5, 6, 7, 8, 9},\)
5 × 6 = 6 × 5 = 30,
5 × 7...