## Professional Information

### Resume

If you have any questions about specific details or would like references, please e-mail me.

### Publications

Includes information about published papers as well as notes, supporting Maple code for various papers, and selected sets of slides from talks.

## Projects

### Good abc Triples Database

A good abc triple is a set of 3 positive integers a, b, c such that

1. a + b = c
2. gcd(a,b,c) = 1
where rad(n) is the product of all primes dividing n for n a positive integer.

The good abc triples database access page currently contains all good abc triples whose c value is less than or equal to 108. The data was generated using python/SAGE scripts. The most recent script is this python/SAGE script which takes between one and two weeks to generate the data on an Opteron PC with 8G of memory.

## Research Notes

### Fibonacci Triangles URAP of Spring 2005.

#### Update: June 2006

This draft includes the work done with David Kettlestrings and proof of the nonexistence of Fibonacci triangles (Fn-k, Fn, Fn) for 5 < k < 10.

During the spring semester of 2005 David Kettlestrings worked with me in the Undergraduate Research Apprenticeship Program on a Fibonacci triangles project. A Fibonacci triangle is a triangle whose area is an integer and whose sidelengths are Fibonacci numbers. An example of a Fibonacci triangle is the triangle whose sidelengths are (5, 5, 8) and it is easy to see that any possible Fibonacci triangle must be isosceles. Harborth, Kemnitz, and Neville have shown any other Fibonacci triangle must be of the type (Fn-k, Fn, Fn) for k> 5 and conjectured that (5, 5, 8) is the only Fibonacci triangle. During the semester David and I have shown that no Fibonacci triangles exist for k=7, 8, 9, 10 as well.