Sum of Odd & Even Integers Always Odd?

[asdf1]

suppose you have 3 integers.
if the intergers are a mixture of odd and even integers, then why does the sum always equal an odd number?

 

[HallsofIvy]

suppose you have 3 integers.
if the intergers are a mixture of odd and even integers, then why does the sum always equal an odd number?

?? 2, 5, 6 is a "mixture of odd and even integers". Their sum is 13 which is odd.

The sum of any two even numbers is even: 2n+ 2m= 2(n+ m).
The sum of any two odd numbers is even: 2n+ 1+ 2m+1= 2n+ 2m+ 2= 2(n+m+ 1).

If a "mixture of odd and even integers" contains an even number of odd integers then it will be even.

But if it contains an odd number of odd integers, it will be odd.

 

[asdf1]

wow~ why is that so?

 

[matt grime]

Look at the definition of odd and even; it's obvious.