# Thread: Proof: Sum of three odd numbers is odd.

1. ## Proof: Sum of three odd numbers is odd.

How do I start?

I know that an odd number can be defined at 2K+1. Would I suppose the result is odd?

2. ## Re: Proof: Sum of three odd numbers is odd.

I would begin by letting the three odd numbers be:

$\displaystyle x=2k_1+1$

$\displaystyle y=2k_2+1$

$\displaystyle z=2k_3+1$

where $\displaystyle k_i\in\mathbb{Z}$

and so:

$\displaystyle x+y+z=?$

3. ## Re: Proof: Sum of three odd numbers is odd.

I think I figured it out. x = (2K+1) y = (2J+1) z = (2Q+1) = 2K+2J+2Q+3 (Factor out 2)

so, 2 (K+J+Q) + 1 is odd by definition and Axiom 2.

Yes?

4. ## Re: Proof: Sum of three odd numbers is odd.

A small point...you should have after factoring, x + y + z = 2(K + J + Q + 1) + 1.