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Filaseta, Michael Anthony 2014-12-16T06:18:11Z 2014-12-16T06:18:11Z 10000-01-01 1984 1984 In this dissertation we present a number of new results in combinatorial number theory. Chapter I discusses a generalization of B(,2)-sequences which are used in Chapter II and Chapter III to obtain short interval results about k-free values of irreducible polynomials. Chapter IV deals with the number of partitions of an integer using a set of distinct parts; Chapter V demonstrates how a single prime value of a polynomial with non-negative coefficients can be used to show that the polynomial is irreducible; Chapter VI compares simple continued fraction convergents for SQRT.(N) with Newton approximations to SQRT.(N); and Chapter VII obtains exact formulas for a certain class of ballot problems. An introduction is included which gives preliminary discussions on various aspects of the problems. Made available in DSpace on 2014-12-16T06:18:11Z (GMT). No. of bitstreams: 1 8502140.pdf: 2428346 bytes, checksum: 0d6d047223eb08bfb4a5b784c8d183ff (MD5) Previous issue date: 1984 Embargo set by: Seth Robbins for item 71391 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 107 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984. http://hdl.handle.net/2142/71225 (UMI)AAI8502140 Mathematics Topics in Combinatorial Number Theory text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.