Abstract
dc:descriptionA 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.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Gibson, Donald Jason
- Contributors dc:contributor
-
- Hildebrand, A.J.
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI3242847
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86867