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oai:www.ideals.illinois.edu:2142/86867 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Hildebrand, A.J. Gibson, Donald Jason 2015-09-28T15:19:55Z 2015-09-28T15:19:55Z 10000-01-01 2006 2006 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. Made available in DSpace on 2015-09-28T15:19:55Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3242847.pdf: 2729567 bytes, checksum: df12c74e93746b2e04e141bee5c993b4 (MD5) Previous issue date: 2006 Embargo set by: Seth Robbins for item 88148 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 100 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. http://hdl.handle.net/2142/86867 (MiAaPQ)AAI3242847 eng Mathematics Covering Systems text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.