MathDB

Defined as

N_0

as the set of all non-negative integers. Set

S \subset N_0

with not so many elements is called beautiful if for every

a, b \in S

with

a \ge b

(

a

and

b

do not have to be different), exactly one of

a + b

a - b

is in

S

. Set

T \subset N_0

with not so many elements is called charming if the largest number

k

such that up to 3

^k | a

is the same for each element

a \in T

. Prove that each beautiful set must be charming.

Problem Statement