IMO 2011 Shortlist A1
For any set A = {a1,a2,a3,a4} of four distinct positive integers with sum sA = a1 +a2 +a3 +a4, let pA denote the number ...
Category: Algebra
Problem
For any set A = {a1,a2,a3,a4} of four distinct positive integers with sum sA = a1 +a2 +a3 +a4, let pA denote the number of pairs (i,j) with 1 ≤ i < j ≤ 4 for which ai +aj divides sA. Among all sets of four distinct positive integers, determine those sets A for which pA is maximal.