Diametrical Points!

A total of $n$ points are equally spaced around a circle and are labelled with the integers $1$ to $n$ , in order. Two points are called diametrically opposite if the line segment joining them is a diameter of the circle. If the points labelled $42$ and $8$ are diametrically opposite, then $n$ equals $\text{\_\_\_\_\_\_\_\_\_\_}$ .

Bonus: Prove that if $n$ is odd, then there are no two points diametrically opposite.