Parity

The integer $n$ is $\text{even}$ if there exists an integer $k$ such that $n=2k$, and $n$ is $\text{odd}$ if there exists an integer $k$ such that $n=2k+1$

Two integers have the $\text{same parity}$ when both are even or both are odd
they have $\text{opposite parity}$ when one is even and the other is odd

$\text{Note that every integer is either odd or even, but not both}$