Files in this item
Files | Description | Format |
---|---|---|
application/pdf ![]() ![]() | (no description provided) |
Description
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 |
This item appears in the following Collection(s)
-
Dissertations and Theses - Mathematics
-
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois