Given any set
of four distinct positive integers, we denote the sum
by
. Let
denote the number of pairs
with
for which
divides
. Find all sets
of four distinct positive integers which achieve the largest possible value of
.
Proposed by Fernando Campos, Mexico
%V0
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 $n_A$.
Proposed by Fernando Campos, Mexico
Školjka