# Can you add 3 odd numbers and get an even number?

The sum of any three odd numbers equals an odd number.

#### Explanation:

Proof

Lets consider three odd numbers

$a = 2 x + 1$
$b = 2 y + 1$
$c = 2 z + 1$

where $a , b , c$ are integers and $x , y , z$ integers as well

then the sum equals to

$a + b + c = 2 \cdot \left(x + y + z + 1\right) + 1$

The last tell us that their sum is an odd.

Sep 17, 2015

Yes, it is possible, but not in ordinary integer arithmetic.

In modular arithmetic with an odd modulus, every number is both odd and even.

#### Explanation:

For example, in arithmetic modulo $7$ we find:

$1 + 3 + 5 = 9 = 2 = 2 \cdot 1$