Question

If a and b are odd positive integers where a greater than b prove that $\frac{a+b}{2}$ always a positive integer.

Answer 1

Since $a$ and $b$ are $2$ positive integers

They can be expressed as $a=2n+1;b=2m+1$ where $n,m$ are integers

So the expression $\frac{a+b}{2}$ takes the form $\frac{2m+1+2n+1}{2}\frac{2m+2n+2}{2}m+n+1$

Since $m.n$ are integers $m+n+1$ is also a integer