MathDB

Let

S = \{x_0, x_1,\dots , x_n\}

be a finite set of numbers in the interval

[0, 1]

with

x_0 = 0

and

x_1 = 1

. We consider pairwise distances between numbers in

S

. If every distance that appears, except the distance

1

, occurs at least twice, prove that all the

x_i

are rational.

Problem Statement