Coast to Coast Seminar Series - Special Session: Live From Halifax, Nova Scotia "A Chinese Prouhet-Tarry-Escott Solution"

Friday, October 12, 2007
11:30 - 12:30

Dr. David Broadhurst
The Open University, UK


Jens Kruse Andersen recently set the challenge of finding complete factorizations of consecutive integers with more than 500 decimal digits. I was able to set records with up to 10 consecutive factorizations by using solutions of the ideal Prouhet-Tarry-Escott (PTE) problem, which is equivalent to finding polynomials with integer roots that differ only by an integer.

PTE solutions with degrees up to s = 10 were known by 1944, but the problem with s > 10 had received only one solution, found almost inadvertently in 1999.

It seemed to me that the ideal PTE problem might benefit from use of the Chinese remainder theorem. I shall describe how a new solution was found at degree s = 12 by the discipline of splitting the problem into a smart part that an be handled by Pari-GP and a brute force part that benefits from parsimonious ForTran programming.