There is a problem with one of the solutions:

Given two real numbers a and b, if ab = 0 then a = 0 and/or b = 0.

So starting with

We see that

or

The second is (almost) trivial, so I'll do the first.

This can only happen when . If you don't see why then expand it:

Now, 2k + 1 is odd, so and .

Thus

The other solution

is correct.

-Dan