A (Not So) Complex Solution to a^2+b^2=c^n

Item

Title

A (Not So) Complex Solution to a^2+b^2=c^n

Description

David F. Putnam Science Center, Room 102

There are formulas that will give all triples of integers a, b, and c that satisfy the Pythagorean Theorem a^2 + b^2 = c^2. It was only recently that it was proved that the equation a^n + b^n = c^n has no integer solutions for a, b, and c when 2 < n. The equation that is the focus of this talk is a combination of these, namely a^2 + b^2 = c^n. The method for producing all solutions will be given along with many examples to illustrate the mathematical process. The surprise is that although the solutions are integers, the techniques involve the use of complex numbers. All preliminary mathematics needed to understand the techniques will be reviewed at the beginning of the talk.

Vincent Ferlini

Contributor

Keene State College

Creator

Kyle G. Averill

Date

2016-04-09

Identifier

https://commons.keene.edu/s/KSCArchive/item/21021

Language

en_US

Subject

Mathematics

Type

Presentation

Rights

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

Item sets

AEC 2016 School of Sciences and Social Sciences

Site pages

School of Sciences and Social Sciences