Prove that is a multiple of 24,
where is an odd number but not divisible by 3.
We have: . is of the form , where is even.
. . That is, for some integer
We see that is divisible 12.
Note that is the product of two consecutive integers.
. . That is, one of them is even, the other odd.
Hence, the product is divisible by 2.
Therefore, is divisible by 24.