MathDB

Two nonnegative integers

a

and

b

are tuanis if the decimal expression of

a+b

contains only

0

and

1

as digits. Let

A

and

B

be two infinite sets of non negative integers such that

B

is the set of all the tuanis numbers to elements of the set

A

and

A

the set of all the tuanis numbers to elements of the set

B

. Show that in at least one of the sets

A

and

B

there is an infinite number of pairs

(x,y)

such that

x-y=1

Problem Statement