In December 2004 I discovered a complete classification of all primes p = 1 (mod 3) such that

   mod p

I am in debt to Andrew Granville for providing proofs.

On Feb 9th I gave a Maple-based talk (which I don't regard as being complete) to the Trinity College Dublin Mathematical Society on some of this work. 

Here are the Maple files of my talk (I didn't get to cover everything...). I had a problem with the html version, and some elements of it may be incomplete:

1. mws format (232KB, output not removed)

2. html format (Maple converts all outputs, in-line equations etc, to gif files, and there are quite a few of those)

I was in the process of writing the work up for submission, but an unfortunate episode in connection with my being external examiner at the Queen's University of Belfast delayed my efforts. Then, at the end of November 2005 I returned, hoping to complete... I thought I just needed to tidy up one small idea, when quite suddenly my work went off in an entirely new direction. To get a very small idea, consult Gauss. I have begun a collaboration with Karl Dilcher, and I expect that Karl and I will produce many papers over the coming years.

Contact details 

After August 31st 2007 please use the following Gmail address: jbcosgrave at gmail.com

This page was last updated 27 August 2007 16:26:18 -0000