A discussion of homogenous quadratic equations

This thesis will look at Quadratic Diophantine Equations. Some well known proofs, including how to compute all Pythagorean triples and which numbers can be represented by the sum of two and four squares will be presented. Some concepts that follow from these theorems will also be presented. These include how to compute all Pythagorean Quadruples, which number can be represented by the difference of two squares and the Crossed Ladders problem. Then, Ramanujan's problem of finding which positive integers, a,b,c and d which allow aw^2+bx^2+cy^2+dz^2 to represent all natural numbers will be shown. The paper will conclude with a lengthy discussion of Uspensky's proof on which numbers can be represented by the sum three squares.

Grantor dc:publisher

Kansas State University

Year dc:date.issued

2009

Author dc:creator

• Kaminski, Lance

• Number Theory
• Diophantine Equations

Statement dc:rights

• © the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/2097/1630

OAI identifier oai:identifier

oai:krex.k-state.edu:2097/1630