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Ahlgren, Scott Reznick, Bruce Prugsapitak, Supawadee 2015-09-28T15:20:13Z 2015-09-28T15:20:13Z 10000-01-01 2009 2009 In this dissertation, we study the Tarry-Escott problem and some related diophantine systems over Z and over some quadratic fields. We give infinitely many solutions of the Tarry-Escott problem over Zi of degrees 2, 3, 4, 5 and 7, none of which can be directly derived from solutions over Z . We show that there are infinitely many solutions of the Tarry-Escott problem of degree 2 over an infinite family of rings Zn . We also solve some diophantine equations which have no integral solutions over some quadratic fields. We partially solve a generalized form of the Tarry-Escott problem of degree 2. Made available in DSpace on 2015-09-28T15:20:13Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3392437.pdf: 1140230 bytes, checksum: c8502bb06ad1a4fbc4dda37640c57e79 (MD5) Previous issue date: 2009 Embargo set by: Seth Robbins for item 88213 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 91 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009. http://hdl.handle.net/2142/86932 (MiAaPQ)AAI3392437 eng Mathematics The Tarry -Escott Problem Over Quadratic Fields text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.