MathDB

Let

S

be a finite, nonempty set of real numbers such that the distance between any two distinct points in

S

is an element of

S

. In other words,

|x-y|

is in

S

whenever

x \ne y

and

x

and

y

are both in

S

. Prove that the elements of

S

may be arranged in an arithmetic progression. This means that there are numbers

a

and

d

such that

S = \{a, a+d, a+2d, a+3d, ..., a+kd, ...\}

Problem Statement