On Representations of integers by the quadratic form x2 − Dy2

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dc.contributor.advisor Agarwal, Anurag
dc.contributor.author Thomas, Christopher
dc.date.accessioned 2012-10-15T16:16:22Z
dc.date.available 2012-10-15T16:16:22Z
dc.date.issued 2012-05-04
dc.identifier.uri http://hdl.handle.net/1850/15377
dc.description.abstract The representation of integers in binary quadratic forms has been a penchant for mathematicians throughout history including the well known Pierre de Fermat and Charles Hermite. The area has grown from simple representations as the sum of squares to representations of the form x²-Dy² where D>1 and square-free. Based on congruence relations we will provide a classification criterion for the integers that can be represented in the form x²-Dy² for various values of D (specifically D=10 and 11). We will also discuss methods for constructing such representations using the theory of continued fractions, quadratic reciprocity and solutions to Pell's equations. en_US
dc.language.iso en_US en_US
dc.subject Diophantine en_US
dc.subject Integer representation en_US
dc.subject Pells equation en_US
dc.subject.lcc QA243 .T46 2012
dc.subject.lcsh Forms, Quadratic en_US
dc.title On Representations of integers by the quadratic form x2 − Dy2 en_US
dc.type Thesis en_US
dc.description.college College of Science en_US
dc.description.department School of Mathematical Sciences en_US

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