## Contents

# PRiME 2010

# Participants

Anyone affiliated with Purdue willing to document project in mathematics is welcome to participate in PRiME. If you want to be added to the official list of participants below, just add yourself. The emphasis of PRiME is to expose the excitement of doing mathematics.

- Matt Davis (Purdue 10' Alumnus)
- James Ryan (Undergraduate Student)
- Jamie Weigandt (Graduate Student)

# Schedule

Monday, July 12, 2010

- 7:30 - 9:30 in MSEE 393: PRiME Kickoff with the Nova Special on Fermat's Last Theorem

Wednesday, July 14, 2010

- Discussed material from chapter 1 of Stein's Book.

Thursday, July 15, 2010

- Discussed euclidean algorithm
- Started sage tutorial

Friday, July 16, 2010

- James Ryan will present the main result which makes the euclidean algorithm work.
- Matt, James, and Jamie will begin discussing Mazur's notices article about the ABC conjecture.
- Start an article about ABC triples

Wednesday, July 21, 2010

- Continue discussing Mazur's article.
- Introduction of the Erdos-Woods Problem

# Research Focus Questions

- Is there an algorithm for deciding the Erdos-Woods Problem?
- If so, is this algorithm practical?
- Can we find *bad* Erdos-Woods examples?
- Can we find *really bad* Erdos-Woods examples?
- Can you catch the Evil Wizard being REALLY EVIL?
- [Jamie] Does every *bad* Erdos-Woods example posses "extra" isogenies?

## Erdos-Woods "Algorithm"

The following are ideas to keep in mind for some type of Erdos-Woods algorithm:

- SPOILER! The trick is to use elliptic curves. :)
- When constructing Frey curves, consider the simplest of $(n,n+1),$ $(n,n+2)$ and $(n+1,n+2).$

## Acknowledgements

The computers used by the students participating in PRiME-Summer 2010 were acquired through the generous support of Intel.