Answer to Question #350691 in Discrete Mathematics for jae

Question

Show that the square of an even number is an even number using a direct proof.

Answer 1

Let $n\in\mathbb{Z}$ - even number, so $n=2z$, where $z\in\mathbb{Z}$.

$n^2=(2k)^2=2^2k^2=2\cdot(2k^2)$ - is an even number because it is divisible by 2.