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