Question 501342
Yes. Here is a proof

First a definition:
multiplying any integer by two gives an even number and adding one to that gives an odd number

Let j=2m+1 and k=2n+1 where m and n are integers. 
Add j and k
j+k=2m+1+2n+1=2m+2n+2=2(m+n)+2
now we can let l=m+n
and j+k=2l+2
From the definition we know that multiplying any integer by two gives an even number and adding one to that gives an odd number.
It should be clear that adding two instead results in an even number.

QED