Electronic Theses and Dissertations

Identifier

1135

Date

2014

Document Type

Thesis

Degree Name

Master of Science

Major

Mathematical Sciences

Concentration

Teaching of Mathematics

Committee Chair

Alistair Windsor

Committee Member

Celia Anderson

Committee Member

Benjamin McCarty

Abstract

Working with the Pythagorean triples in Number Theory class, I became intrigued by several attributes within this special set of numbes. Therefore, I will be investigating and validating the following characteristics of the Pythagorean triples:1) A Pythagorean triple consists of either one even number along with two odd numbers or three even numbers.2) Every Pythagorean triple contains a multiple of 3, a multiple of 4, and a multiple of 5.3) Every odd number greater than 1 is part of a Twin Pythagorean triple.4) All Natural numbers greater than 2 appear at least once in a Pythagorean triple and several numbers appear in two or more distinct triples.5) Every prime number of the form 4k + 1 is a hypotenuse of a Pythagorean triple.6) The smallest value of c for which there exist four distinct solutions with a, b, and c pairwise co-prime is 1105.

Comments

Data is provided by the student.

Library Comment

Dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.

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