#### 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 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.

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 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.