# Euler on Little Fermat and Fermat's Conjecture

## Presenter(s)

Chloe M. Crabb

Presentation: 11:40 a.m.-12:00 p.m., Kennedy Union 207

## Description

For centuries, mathematicians have been exploring the idea of prime numbers. How do we find them? Are there techniques that guarantee the existence of primes? While it is relatively easy to verify the factors of a number today using computers and programs, this was no small task in the in the 18th century or any time before that. Pierre de Fermat was famous for his contributions to number theory but was notorious for leaving the proofs as exercises for others. Two such theorems include “Little Fermat,” which states if p is prime and a is a whole number which does not have p as a factor, then p divides evenly into a^(p+1)-1, and his conjecture that 2^(2^n)+1 is prime. Here we will explore Euler’s proof of “Little Fermat” and run through how he refutes Fermat’s conjecture.

4-20-2022

## Project Designation

Capstone Project

Rebecca J. Krakowski