MathDB

Given

8

pairwise distinct positive integers

a_1,a_2,…,a_8

such that the greatest common divisor of any three of them is equal to

1

. Show that there exists positive integer

n\geq 8

and

n

pairwise distinct positive integers

m_1,m_2,…,m_n

with the greatest common divisor of all

n

numbers equal to

1

such that for any positive integers

1\leq p<q<r\leq n

, there exists positive integers

1\leq i<j\leq 8

that

a_ia_j\mid m_p+m_q+m_r

Problem Statement