Question 6
a) Does there exist a set $A$ that has $2016$ pairwise different positive integers and such a property: for every non-empty subset $B \subset A$ that is not equal to $A$ and every non-empty subset $C \subset (A \setminus B)$ the sum of the elements of subset $B$ is not divisible by the sum of the elements of subset $C$?
b) Does there exist a set $A$ that has $2016$ pairwise different positive integers and such a property: for every non-empty subset $B \subset A$ that is not equal to $A$ and contains at least $2$ elements and every non-empty subset $C \subset (A \setminus B)$ the product of the elements of subset $B$ is divisible by the sum of the elements of subset $C$?
b) Does there exist a set $A$ that has $2016$ pairwise different positive integers and such a property: for every non-empty subset $B \subset A$ that is not equal to $A$ and contains at least $2$ elements and every non-empty subset $C \subset (A \setminus B)$ the product of the elements of subset $B$ is divisible by the sum of the elements of subset $C$?