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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 = 7 × 5 = 35,
5 × 8 = 8 × 5 = 40,
5 × 9 = 9 × 5 = 45,
6 × 7 = 7 × 6 = 42,
6 × 8 = 8 × 6 = 48,
6 × 9 = 9 × 6 = 54,
7 × 8 = 8 × 7 = 56,
7 × 9 = 9 × 7 = 63,
8 × 9 = 9 × 8 = 72,
and the required cardinality is 10.
I have not been able to solve it.
Apologies for not posting the problem here as could not resolve latex issues. Someone please post the problem here.
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 = 7 × 5 = 35,
5 × 8 = 8 × 5 = 40,
5 × 9 = 9 × 5 = 45,
6 × 7 = 7 × 6 = 42,
6 × 8 = 8 × 6 = 48,
6 × 9 = 9 × 6 = 54,
7 × 8 = 8 × 7 = 56,
7 × 9 = 9 × 7 = 63,
8 × 9 = 9 × 8 = 72,
and the required cardinality is 10.
I have not been able to solve it.
Apologies for not posting the problem here as could not resolve latex issues. Someone please post the problem here.