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.

Also see Odd Integer 2n + 1.


 * 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.