Problem: If is a prime number, then 24 divides without remainder
Answer Choices:
A.
B. Sometimes only
C.
D. only if
E. None of these
Solution:
Since the factors and of are consecutive even integers, both are divisible by and one of them also by so that their product is divisible by . Again and are three consecutive integers so that one of them (but not the prime ) is divisible by . Hence the product is always divisible both and and hence by .