MathDB

Let

F

be a finite subset of the integer numbers. We define a new subset

s(F)

in that

a\in Z

lies in

s (F)

if and only if exactly one of the numbers

a

and

a -1

F

. In the same way one gets from

s (F)

the set

s^2(F) = s (s (F))

and by

n

-fold application of

s

then iteratively further subsets

s^n (F)

. Prove there are infinitely many natural numbers

n

for which

s^n (F) = F\cup \{a + n|a \in F\}

Problem Statement