Posted by **Steve** on Saturday, April 6, 2013 at 11:26pm.

If a and b are positive odd integers, then prove that one of (a+b)/2 and (a-b)/2 are even or odd number. I mean in the above numbers one is odd and one is an even number.

- Math -
**black_widow**, Sunday, April 7, 2013 at 10:12am
Let a>b

a=2n+1+2k ,n,k is positive

b=2n+1

(a+b)/2=2n+1+k

(a-b)/2=k

If k is odd,

then

(a+b)/2 is even

(a-b)/2 is odd

If k is even,

(a+b)/2 is odd

(a-b)/2 is even

The same method also applies if a<b

(However I assume that a,b are distinct number because if a=b, (a-b)/2=0 but 0 is neither odd nor even)

- Math - to black_widow -
**Steve**, Sunday, April 7, 2013 at 12:51pm
excuse me? 0 is an even number. The definition of even is that it leaves a zero remainder when divided by 2.

- Math -
**black_widow**, Friday, April 12, 2013 at 10:30pm
sorry about that....

I thought 0 is neither even nor odd....

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