Ovals In a Finite Projective Plane

1. Let be a finite projective plane (8, §17), i.e. a projective space of dimension 2 over a Galois field γ. We suppose that γ has characteristic p ≠ 2, hence order q = pn , where p is an odd prime and h is a positive integer. It is well known that every straight line and every non-singular conic of then contains q + 1 points exactly.