Hello, dlee426!

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

Then: .

And: .

We see that is divisible 12.

Note that is the product oftwo consecutive integers.

. . That is, one of them is even, the other odd.

Hence, the product is divisible by 2.

Therefore, is divisible by 24.