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2011 IMO Shortlist Problems/A1

Revision as of 05:44, 28 October 2013 by DANCH (talk | contribs) (Created page with "==Problem== Given any set <math>A = \{a_1, a_2, a_3, a_4\}</math> of four distinct positive integers, we denote the sum <math>a_1 +a_2 +a_3 +a_4</math> by <math>s_A</math>. Let <...")
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Problem

Given any set $A = \{a_1, a_2, a_3, a_4\}$ of four distinct positive integers, we denote the sum $a_1 +a_2 +a_3 +a_4$ by $s_A$. Let $n_A$ denote the number of pairs $(i, j)$ with $1 \leq i < j \leq 4$ for which $a_i +a_j$ divides $s_A$. Find all sets $A$ of four distinct positive integers which achieve the largest possible value of $n_A$.

Author: Fernando Campos, Mexico

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