3. For each positive integer n, let Sn be the set that contains the integers from 1 to n, inclusive; that is, Sn = {1, 2, 3, ..., n}. For each positive integer n 2 4, let f(n) be the number of quadruples (a, b, c, d) of distinct integers from Sn for which a - b = c - d. For example, f(4) = 8 because the possibilities for (a, b, c, d) are (1, 2, 3, 4), (1, 3, 2, 4), (2, 1, 4, 3), (2, 4, 1, 3), (3, 1, 4, 2), (3, 4, 1, 2), (4, 2, 3, 1), (4, 3, 2, 1) (a) Determine the value of f(6). (b) Determine the value of f(40). (c) Determine two even positive integers n