The n-dimensional finite projective space, P G(n, q), admits a cyclic model, in which the set of points of P G(n, q) is identified with the elements of the group Z q n +q n−1 +···+q+1. It was proved by Hall (1974, Math. Centre Tracts, 57, 1–26) that in the cyclic model of P G(2, q), the additive inverse of a line is a conic. The following generalization of… (More)
In this paper, after presenting the results of the generalization of Pascal triangle (using powers of base numbers), we examine some properties of the 112-based triangle, most of all regarding to prime numbers. Additionally, an effective implementation of ECPP method is presented which enables Magma computer algebra system to prove the primality of numbers… (More)
The notion of successive illumination parameters of convex bodies is introduced. We prove some theorems in the plane and determine the exact values of the successive illumination parameters of spheres, cubes and cross-polytopes for some dimensions.
Semiovals in PG(2, q) for q ≤ 13 are investigated. New examples are constructed, some characterization theorems and non-existence results of semiovals with extra properties are proved.