F(n, p) =

^{n}C

_{p}- ⌊n/p⌋

where n is a positive integer and p is a prime number.

Is F(n, p) always divisible by p?

If so, prove it.

If not, provide a counterexample.

__Notes:__ ^{n}C_{p} is the number of combinations of n elements taken p at a time. It is also known as Binomial Coefficient and read as "n choose p".

• ⌊m⌋ is equal to floor of m which is the greatest integer less than or equal to m