Consider the following statement and its "proof". 

If m is an even integer and n is an odd integer, then 3m + 5n is odd.

Proof. 

1. Let m be an even integer and n an odd integer. 
2. Then there is an integer k such that m = 2k and n = 2k +1.  
3. Therefore 3m + 5n = 3(2k) + 5(2k + 1) = 16k+5 = 2(8k+2)+1
4. Since 8k + 2 is an integer, 3m + 5n is odd.

Which of the following is correct?