| 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 Erdős. 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 covering systems are defined in Fq[x]. Examples of covering systems in the particular case of F2[x] are presented along with some restrictions as to their construction. Also presented is a conjecture concerning covering systems of F 2[x] analogous to one of Erdős concerning covering systems of the integers. |
