proofs #3

claim

300

The claim for problem #3.

If m is even, then 6m + 3 is odd

proof

100

The proof for problem #3.

Assume m is even.

definitions

300

The definitions for problem #3.

This means m=2x for any integer x.

logic

400

The logic for problem #3.

Consider 6m + 3. 

6m+3 = 6(2x)+3

12x+3=12x+2+1

2(6x+1)+1

creativity

500

The creativity for problem #3.

But, 6x+1 is just another integer, call it z. 

So, 2z+1 = 6m+3