# Difficulty in understanding a number theory problem

So here's the problem:-

Find four distinct positive integers whose product is divisible by the sum of every pair of them.

I am having difficulty understanding what this means, as it can be interpreted 2 ways-

1. Find positive integers a,b,c,d such that ab+ac+ad+bc+bd+cd divides a abcdii

2. Find positive integers a,b,c,d such that:-

a+b divides abcd

a+c divides abcd

a+d divides abcd

b+c divides abcd

b+d divides abcd

c+d divides abcd

Which way is correct?

• I think number 2. – Arthur Sep 3 '18 at 5:42

This definitely means interpretation (2) (except that you have left out the pair $a+d$). To get interpretation (1), it would need to instead say "the sum of the products of every pair of them". As written, it never mentions anything about multiplying the numbers in the pairs.