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Covering Systems Of Polynomial Rings Over Finite Fields, Michael Wayne Azlin

Electronic Theses and Dissertations

In 1950 Paul Erdos observed that every integer belonged to a certain system of congruences with distinct moduli. He called such systems of congruences covering systems. Utilizing his covering system, he disproved a conjecture of de Polignac asking, “for every odd k, is there a prime of the form 2n + k?” Examples of covering systems of the integers are presented along with some brief history and a sketch of the disproof by Erd?s. Open conjectures concerning covering systems and best known results of attempts to prove these conjectures are given. Analogies are drawn between the integers and Fq[x], and …