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Dmoz: Science: Math: Number Theory: Diophantine Equations: Equal Sums of Like Powers

- Equal Sums of Like Powers - Chen Shuwen's extensive collection of equal sums of like powers, especially those that are solutions to multigrade equations.
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Number Theory Web: Descriptions of areas/courses in number theory, lecture notes

- Equal Sums of Like Powers/Tarry Escott Problem: Chen Shuwen's Page

- The definite link for all multigrade equations ! (Chen Shuwen)
- You can find a mirror of his page here.

- Mathematics Archives - Topics in Mathematics - Number Theory
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- Sommes Multipuissantes (French)
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- Multi Sommes de Puissances (French)
- Palindromic Squares

`Mail Selcetion during
1997/7-1999/12`

Subject: FYI: Your site chosen as an Open Directory Cool Site

- Date: Thu, 9 Sep 1999 00:15:23 -0700
- From: Warut Roonguthai
- To: jmchen@pub.jiangmen.gd.cn
- CC: warut@ksc9.th.com, admin@dmoz.org
- This is to inform you that the website
- http://member.netease.com/~chin/eslp/eslp.htm
- has been designated a Cool Site in the Netscape Open Directory
- Science/Math/Number_Theory/Diophantine_Equations/Equal_Sums_of_Like_Powers
- category at
- http://dmoz.org/Science/Math/Number_Theory/Diophantine_Equations/Equal_Sums_of_Like_Powers/

- Date: Tue, 07 Sep 1999 15:56:24 -0700
- From: Ian Barrodale
- To: jmchen@pub.jiangmen.gd.cn
- At 02:00 AM 9/8/99 +0800, you wrote:
- >Ideal solutions of the the Prouhet-Tarry-Escott problem has been solved for
- >the k=11 case recently. That is
- > [ 0, 11, 24, 65, 90, 129, 173, 212, 237, 278, 291, 302 ]
- >= [ 3, 5, 30, 57, 104, 116, 186, 198, 245, 272, 297, 299 ]
- Congratulations!! How was this found? Did you find it?
- Is there a degree 10 ideal solution yet?
- Regards,
- Ian Barrodale

- Date: Tue, 7 Sep 1999 17:28:15 -0700 (PDT)
- From: Peter Borwein
- To: jmchen@pub.jiangmen.gd.cn
- Congratulations. This is very exciting.
- How did you find the intermediate solution that you used?
- Sincerely,
- Peter Borwein

- Date: Wed, 08 Sep 1999 07:40:05 -0400
- From: Steven Finch
- To: jmchen@pub.jiangmen.gd.cn
- Dear Chen Shuwen,
- Congratulations!
- Steve Finch

- Date: Thu, 9 Sep 1999 14:08:34 +0700 (ICT)
- From: Warut Roonguthai
- To: Chen Shuwen <jmchen@pub.jiangmen.gd.cn>
- Hearty congratulations! Very impressive indeed!
- Best wishes,
- Warut

- Date: Thu, 09 Sep 1999 21:00:51 +0100
- From: Richard Walker
- To: jmchen@pub.jiangmen.gd.cn
- 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

- Date: Sun, 12 Sep 99 10:30:58 CET
- From: A.Schinzel
- To: jmchen@pub.jiangmen.gd.cn
- Dear Dr.Chen,
- My warm congratulations on solving the Prouhet-Tarry-Escott problem for k=11.
- Andrzej Schinzel

- Date: Wed, 15 Sep 1999 10:20:56 +0100
- From: Chris Smyth
- 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.)
- Best wishes
- Chris Smyth

- Date: Thu, 16 Sep 1999 10:35:04 -0500
- From: Underwood Dudley
- To: jmchen@pub.jiangmen.gd.cn
- Dear Professor Chen:
- 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.
- Underwood Dudley
- Editor, CMJ
- Date: Thu, 16 Sep 1999 20:43:56 -0500
- From: Underwood Dudley
- To: jmchen@pub.jiangmen.gd.cn
- >please include Nuutti Kuosa and Jean-Charles Meyrignac's name also.
- I'll do that. Thank _you_.
- Woody Dudley

- I have included links to it in
my (
*Number Theory Web*)*New Listings*and*Descriptions of areas/courses in number theory, lecture notes/virtual study groups*and*Complete List*. By the way, are you familiar with*Unsolved Problems in Number Theory*(Second Edition), R.K. Guy, Problem Books in Mathematics, Springer 1994, ISBN 3-540-94289-0. It has some information relevant to your problems in section D1. Also there is Hardy and Wright. Perhaps it might be a good idea to include references to these and other papers on the subject.

Kevin Brown ( ksbrown@seanet.com )

- 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.

- Thanks for sending the URL to your interesting home page. You've done a good job of presenting your results.

Earl D. Fife ( fife@calvin.edu )

- You will find the link (to your
site) located in
*Mathematics Archives - Topics in Mathematics - Number Theory*.

Joseph H. Silverman ( jhs@math.brown.edu )

- I looked at your "sums of equal powers" pages and found them very interesting.

Simon Plouffe ( plouffe@cecm.sfu.ca )

- 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.

Aleksandrs Mihailovs ( mihailov@math.upenn.edu )

- Indeed, your page is extremely interesting.

Aleksandrs Mihailovs ( mihailov@math.upenn.edu )

- I put the link to your page on
my
*Alec Mihailovs's Research Page*.

Steven Finch ( sfinch@mathsoft.com )

- When your page
*Unsolved problems and conjectures*is completed, please e-mail me. This is most likely the page I will want to link to from my*Unsolved Mathematics Problems*page.

Giuseppe Melfi ( melfi@dm.unipi.it )

- Very many thanks for your interesting site.

Eric W. Weisstein ( eww6n@carina.astro.virginia.edu )

- Thanks very much for letting me
know about your very nice page. I'll be looking at it carefully over the
next few days any perhaps adding some of the material to my pages. (
*Eric's Treasure Trove of Mathematics - Diophantine Equation*,*Multigrade Equation*)

Lev Vsevolod ( seva@math.tau.ac.il )

- I discovered your page a few days before. It looks exciting, though not quite in my line.

Josef Eschgfaeller ( esg@felix.unife.it )

- I put you on
*Mathematical BBS - Number theory*under Diophantine equations, as Chen Shu-wen.

- Excellent page!! I very much enjoyed your homepage.

- I have added a link ( on
*MathPages - Links to Other Sites*) to your site now.

- I certainly think it is a very interesting problem, and the examples you have found are quite beautiful.

- 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.

Chris Smyth ( chris@maths.ed.ac.uk )

- 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.

Jun Xu ( junxu@cs.uh.edu )

- Your home page is very impressive!

David M. Bressoud ( bressoud@macalester.edu )

- It does appear that you have done some very interesting mathematics.

Tom Verhoeff ( wstomv@win.tue.nl )

- I have added a link from the page
for
*International Mathematics Olympiads*at the*IOI Secretariat*to your page. It looks very interesting.

Allen Freeman ( acf8v@virginia.edu )

- Although I am not a mathmatician, I am a history teacher, I am interested ( to your site ). I will pass your note to my friends.

Sinan Sertoz ( sertoz@fen.bilkent.edu.tr )

- 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.

- Your site is a great example of the web being used as a meeting place of mathematical ideas. It is a great model to follow.

- The new version of Equal sums of like powers is quiet well. I read it carefully. A very good job indeed.

- We are using your page for our reference at http://www.jiangmen.gd.cn/person/chen/eslp.htm
- This is really a great page and we should present our thanks to you , for making such studies in the name of the mathematical society.

- 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.

- Congratulations on your very interesting pages and the many beautiful results you present.

Copyright 1997-2001, Chen Shuwen