MathDB

Let S be a finite set of non-negative integers such that

| x - y | \in S

whenever

x , y \in S

. (a) Give an example of such a set which contains ten elements. (b) If

A

is a subset of

S

containing more than two-thirds of the elements of

S

, prove or disprove that every element of

S

is the sum or difference of two elements from

A

Problem Statement