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 Title: The Tarry -Escott Problem Over Quadratic Fields Author(s): Prugsapitak, Supawadee Doctoral Committee Chair(s): Ahlgren, Scott; Reznick, Bruce Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: 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. Issue Date: 2009 Type: Text Language: English Description: 91 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009. URI: http://hdl.handle.net/2142/86932 Other Identifier(s): (MiAaPQ)AAI3392437 Date Available in IDEALS: 2015-09-28 Date Deposited: 2009
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