Muatazz Abdolhadi Bashir, Andrew Rajah
Abstract
In this paper we investigate the non-existence of a projective plane of order 12 by using the relationship between Latin squares and projective planes. We arrive at a conjecture: if the sum of all divisors of a positive integer n, (n) > 2n, then there is no finite projective plane of order n.
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In this paper we investigate the non-existence of a projective plane of order 12 by using the relationship between Latin squares and projective planes. We arrive at a conjecture: if the sum of all divisors of a positive integer n, (n) > 2n, then there is no finite projective plane of order n.
Key concepts: Projective plane, Mathematics, Blocking set, Projective test, Real projective plane, Finite geometry, Collineation, Conjecture