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A discussion of homogenous quadratic equations

Master of Science / Department of Mathematics / Christopher G. Pinner / 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.

Identiferoai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/1630
Date January 1900
CreatorsKaminski, Lance
PublisherKansas State University
Source SetsK-State Research Exchange
Languageen_US
Detected LanguageEnglish
TypeThesis

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