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Question 501342: If two numbers are odd, then is their sum even?
Answer by Mr_Mathman(5)   (Show Source):
You can put this solution on YOUR website! 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
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