Definition:Parity of Integer

Definition

Let $z \in \Z$ be an integer.

The parity of $z$ is whether it is even or odd.

That is:

an integer of the form $z = 2 n$, where $n$ is an integer, is of even parity;
an integer of the form $z = 2 n + 1$, where $n$ is an integer, is of odd parity.

If $z_1$ and $z_2$ are either both even or both odd, $z_1$ and $z_2$ have the same parity.
If $z_1$ is even and $z_2$ is odd, then $z_1$ and $z_2$ have opposite parity.