Problem: If is any whole number, is always divisible by:
Answer Choices:
A.
B.
C. Any multitude of
D.
E. and
Solution:
By considering the special case we immediately rule out choices (B), (C), (D), and (E). We now show that (A) holds.
where is a product of three consecutive integers, hence always divisible by . If is even, is divisible also by (since is a factor of ), hence by , and by ; if is odd, is divisible also by (since the even numbers and are factors of ), hence by .