If you have any questions about specific details or would like
references, please e-mail me.
Includes information about published papers as well as notes, supporting
Maple code for various papers, and selected sets of slides from talks.
A good abc triple is a set of 3 positive integers a, b, c such that
where rad(n) is the product of all primes dividing n for n a
- a + b = c
- gcd(a,b,c) = 1
- c > rad(abc)
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
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.