On pythagorean triples modulo a prime

Date of Publication

2016

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Rigor B. Ponsones

Abstract/Summary

This paper is an exposition of the article entitled Pythagorean Triples Modulo a Prime by Bernard Moore and Joseph Straight which was published in the Pi Mu Epsilon journal [1]. It discusses the existence and number of solutions to the equation x2 +y2 z2 (mod p), where p is a prime greater than or equal to 7 and x, y, and z are elements of the multiplicative group Z#p = f1 2 : : : p {u100000} 1g modulo p. A program was created to compute quadratic residues, siblings of c, distinct values of a and b for a given c to generate Pythagorean triple (a b c) (mod p), Pythagorean triples, quadratic residue, siblings, isosceles Pythagorean triples and number of non-equivalent solutions for prime p.

Abstract Format

html

Language

English

Format

Electronic

Accession Number

CDTU021106

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Keywords

Pythagorean theorem; Triples, Theory of; Congruences and residues; Health

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