## Electronic Theses and Dissertations

1135

2014

4-29-2014

Thesis

#### Degree Name

Master of Science

#### Major

Mathematical Sciences

#### Concentration

Teaching of Mathematics

Alistair Windsor

Celia Anderson

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.