Covering Systems

Gibson, Donald Jason

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Title:	Covering Systems
Author(s):	Gibson, Donald Jason
Doctoral Committee Chair(s):	Hildebrand, A.J.
Department / Program:	Mathematics
Discipline:	Mathematics
Degree Granting Institution:	University of Illinois at Urbana-Champaign
Degree:	Ph.D.
Genre:	Dissertation
Subject(s):	Mathematics
Abstract:	A collection of congruences with distinct moduli, each greater than 1, such that each integer satisfies at least one of the congruences, is said to be a set of covering congruences, or covering system. A famous conjecture of Erdos from 1950 states that the least modulus of a covering system can be arbitrarily large. This conjecture remains open, and, in its full strength, appears at present to be unattackable. Most of the effort in this direction has been aimed at explicitly constructing covering systems with large least modulus. Improving upon previous results of Churchhouse, Krukenberg, Choi, and Morikawa, we construct a covering system with least modulus 25. The construction involves a large-scale computer search, in conjunction with two general results that considerably reduce the complexity of the search.
Issue Date:	2006
Type:	Text
Language:	English
Description:	100 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006.
URI:	http://hdl.handle.net/2142/86867
Other Identifier(s):	(MiAaPQ)AAI3242847
Date Available in IDEALS:	2015-09-28
Date Deposited:	2006