... if you go back and dig up crap from a year ago, you must be pretty hard up.

Your "proof" assumes the "proof" that it sets out to "prove" as the foundation for the "proof". You started out with "Every even number X can be expressed as (2 * N) for some other number N.". Therefore, you are just chasing your tail in an endless loop.

Now, trot along and go bite someone else's ankles, sonny boy, for the truth of the matter is that you are clueless about Fermat's Last Theorem, but you are pretty good at googling because you have nothing else going for you.

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Every even number X can be expressed as (2 * N) for some other number N.
Every odd number Y can be expressed as ( 2 * N) + 1 for some other number N.

If a number can be expressed as (2 * N), it is an even number.
If a number can be expressed as (2 * N) + 1, it is an odd number.

The product of an even number X and an odd number Y is written: X * Y

Since X is an even number, this can be rewritten as:
X * Y = (2 * M) * Y

By the associative property of multiplication, this can be rewritten as:
X * Y = (2 * M) * Y = 2 * (M * Y)

We can express (M * Y) as N, yielding:
X * Y = (2 * M) * Y = 2 * (M * Y) = 2 * N

Thereby proving that the product of an even number and an odd number is always an even number.

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