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....

## Answer This Question

## Related Questions

- discrete math - prove that if n is an integer and 3n+2 is even, then n is even ...
- discrete math - use a direct proof to show that the product of two odd numbers ...
- Algerbra - f m and p are positive integers and (m + p) x m is even, which of the...
- Geometry - CounterExamples and Inductive Reasoning and Conjectures? Make a ...
- odd and even functions - Using f is odd if f(-x) = -f(x) or even if f(-x) = f(x...
- Maths - The first odd number can be expressed as 1 = 1squared - 0squared. The ...
- math - Let f:ℤ+ → ℤ+ be the function defined by: for each x &#...
- math help please - Let f:ℤ+ → ℤ+ be the function defined by: ...
- discrete math - Let f:ℤ+ → ℤ+ be the function defined by: for...
- Geometry - Working on conjectures. The question is Conjecure: The product of any...

More Related Questions