Y by Mango247
For a finite set
of integers, define
as the number of values obtained by adding any two elements of
, not necessarily different. Analogously, define
as the number of values obtained by subtracting any two elements of
, not necessarily different.
For example, if
The values obtained by adding any two elements of
are
and so
.
The values obtained by subtracting any two elements of
are
and as
.
Prove that for each positive integer
there is a finite set
of integers such that
.





For example, if









Prove that for each positive integer


