Why is $ab=(a-b)(a+b)$ false when $a,b$ are coprime? I could not find this, and do not have a background in number theory so sorry if this sounds trivial.
If $a$ and $b$ are coprime integers, why is the statement
$$ab=(a-b)(a+b)$$
a contradiction?

If $a$ and $b$ are coprime integers and $ab=(a-b)(a+b)$, then either $a$ is even and $b$ is odd or the other way round. In any case, $ab$ would be even while $(a-b)(a+b)$ would be odd, quod est absurdum.
