ABSTRACT
A non-singular conic of the projective plane PG(2, q) over the Galois field GF(q) consists of q + 1 points no three of which are collinear. It is natural to ask if this non-collinearity condition for q + 1 points is sufficient for them to be a conic. In other words, does this combinatorial property characterise non-singular conics? For q odd, this question was affirmatively answered in 1954 by Segre [44, 45].388
