Equal Sums of Like Powers - Chen Shuwen's extensive
collection of equal sums of like powers, especially those that are solutions
to multigrade equations.
I have looked at the site and this
is indeed a remarkable discovery. Previous computer searches for a solution
to the k=11 case were unsuccessful, so this is a big surprise and great
progress!
Regards,
Richard Walker
Subject: Re: Great Progress on
the Prouhet-Tarry-Escott problem!
Organization: Maths&Stats Dept, Edinburgh
University
To: jmchen@pub.jiangmen.gd.cn
Dear Chen,
Many thanks for your message about
the ideal example for k=11.
I'm really surprised at how small
the numbers are.
I also noticed that the product
of the second set of numbers (3,5,...,299) is divisible only by the primes
up to 31, and no more. But maybe this is a result of how the search was
conducted. (I didn't look at details of that.)
Congratulations for finding a solution
to the Tarry-Escott-Prouhet problem for n = 11! Would it be all right with
you if I included a paragraph about it in an early issue (probably January)
of the _College Mathematics Journal_? I'll include your e-mail web site
addresses unless you'd rather I didn't.
I'm aware of some results on sums
of equal powers as listed in Dickson's "History of the Theory of
Numbers", where he describes some parametric solutions, usually
for consecutive exponents k=1,2,3,..,n, with m=n+1. You obviously have
solutions that go beyond those listed in Dickson. I'm particularly interested
in your solutions for non-consecutive sequences of exponents.
I think that it is (indeed) an
interesting number theory question. If I may I will forward the URL of
your page to a math discussion group and they will (pretty sure), appreciate.
I visited your equal sum home page
and find it amazing that you have found and collected so many formulas.
Unfortunately I am not an expert in this field and could not give more
precise comments. Hope your work will continue to be productive and inspiring.
I've had a look at your 'equal
sums of like powers' pages, and they are very informative. It's a good
service to the math community to do that. It'll be the first port of call
for anyone working on the subject in the future.
I appreciated the difficulty and
the beauty of your work. I am working on algebraic geometry most of the
time but sometimes I do work on Frobenius problem. I forwarded your mail
to a friend who works more in number theory. I wish you increasing success
in your work.
Until 18'th century, nine discoveries
out of ten was accepted as Chinese origin. After seing your immense intellectual
work; I now understand why it was so , In these studies we see the power
of Chinese Ingenuity as well as oriental perfectness and mystical beauty.
Just continue your work in numbers theory, since it really enlightens our
mathematical world society like the works of your ancestors once made.....
a member of Time Traveler (sci. & math. Org)
It is difficult to add something
to your Dreambook after Haracci (from Time Traveler Org.) I was so impressed,
that I checked her home page and added it just after yours to my research
page.