2011 IMO Problems/Problem 1
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Given any set A = {a1, a2, a3, a4} of four distinct positive integers, we denote the sum a1+a2+a3+a4 bysA. Let nA denote the number of pairs (i,j) with 1 ≤ i< j ≤ 4 for which ai+aj divides sA. Find all sets A of four distinct positive integers which achieve the largest possible value of nA.
