Use the definition of the binomial coefficient to establish the following:
-
.
- If
find
.
- If
find
.
- Is there an integer
such that
?
-
Proof. By definition we have,
-
Using part (a) we know
. So, if
and
, then
.
-
Again, by part (a) we have
implies
.
-
No. Since
implies
is not an integer.