For a given positive integer n (n ≥ 6), set a is composed of the sum of five consecutive positive integers not greater than N, and set B is composed of the sum of six consecutive positive integers not greater than n If the number of elements of a ∩ B is 2013, then the maximum value of n is?

For a given positive integer n (n ≥ 6), set a is composed of the sum of five consecutive positive integers not greater than N, and set B is composed of the sum of six consecutive positive integers not greater than n If the number of elements of a ∩ B is 2013, then the maximum value of n is?

Let a = {5A + 10 | a = 1,2,..., n-4}, B = {6B + 15 | B = 1,2,..., N-5} let x ∈ a ∩ B, then x = 5A + 10 = 6B + 15 = > 5 (A-1) = 6B = > b is a multiple of 5, let B = 5K, then x = 30K + 15,5k ≤ N-5 ∩ it is easy to know that a ∩ B = {x | x = 30K + 15,1 ≤ K ≤ (N-5) / 5 and K is an integer} ∩ the number of a ∩ B [(N-5) / 5]