Definition Suppose is an integer. If there exists an integer such that , then is an odd number. If there exists an integer such that , then is an even number.

The concept of even and odd numbers are most easily understood in the binary base. Then the above definition simply states that even numbers end with a 0, and odd numbers end with a .

Properties

1. Every integer is either even or odd. This can be proven using induction, or using the fundamental theorem of arithmetic.
2. An integer is even (odd) if and only if is even (odd).