Let SK 1+2+...+K / K and ∑ S^2 j = n/A ; x ∈ (n, j=1)

Question

Let \(s_K\frac{1+2+...+K}{K}\) and \(\displaystyle\sum_{j=1}^{n}S^2_j=\frac{n}{A}\) (Bn2 + Cn+D), where A, B, C, D ∈ N and A has least value. Then

(1) A + B is divisible by D 

(2) A + B = 5 (D –C) 

(3) A + C + D is not divisible by B 

(4) A + B + D is divisible by 5

Answer 1

(1) A + B is divisible by D

A = 24, B = 2, C = 9, D = 13