# Integer Proof

• Mar 1st 2009, 11:35 AM
noles2188
Integer Proof
I need help with the following proof

Prove: If each of m and n is an integer, then m+n and m-n are both even if m and n are both even or both odd.
• Mar 1st 2009, 12:09 PM
GaloisTheory1
Quote:

Originally Posted by noles2188
I need help with the following proof

Prove: If each of m and n is an integer, then m+n and m-n are both even if m and n are both even or both odd.

hint: even - write as $m=2k$, $n=2l$ [ $k,l \in \mathbb{Z}$], then finish.

odd - write as $m=2k+1$, $n=2l+1$ [ $k,l \in \mathbb{Z}$], then finish.