Wilson's Theorem/Necessary Condition/Proof 2

Proof
If $p = 2$ the result is obvious.

Therefore we assume that $p$ is an odd prime.

Consider $p$ points on the circumference of a circle $C$ dividing it into $p$ equal arcs.

By joining these points in a cycle, we can create polygons, some of them stellated.

From Number of Different n-gons that can be Inscribed in Circle, the number of different such polygons is $\dfrac {\paren {p - 1}!} 2$.