Presentation Title

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

Presentation Type

Oral Presentation

School

School of Sciences and Social Sciences

Discipline

Mathematics

Mentor

Vincent Ferlini

Date & Time

April 9th at 9 AM - 10 AM

Location

David F. Putnam Science Center, Room 102

Abstract

There are formulas that will give all triples of integers a, b, and c that satisfy the Pythagorean Theorem a2 + b2 = c2. It was only recently that it was proved that the equation an + bn = cn 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 a2 + b2 = cn. 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.

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Apr 9th, 9:00 AM Apr 9th, 10:00 AM

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

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 a2 + b2 = c2. It was only recently that it was proved that the equation an + bn = cn 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 a2 + b2 = cn. 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.