MathDB

Let

\mathcal{S}

be a set consisting of

n \ge 3

positive integers, none of which is a sum of two other distinct members of

\mathcal{S}

. Prove that the elements of

\mathcal{S}

may be ordered as

a_1, a_2, \dots, a_n

so that

a_i

does not divide

a_{i - 1} + a_{i + 1}

for all

i = 2, 3, \dots, n - 1

Problem Statement