# Equal Sums of Like Powers

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

Number Theory Web: Descriptions of areas/courses in number theory, lecture notes

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

Computing Minimum Equal Sums Of Like Power: Links
You can find a mirror of his page here.

Mail Selcetion during 1997/7-1999/12

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

Subject: Re: Great Progress on the Prouhet-Tarry-Escott problem!
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 ]
Is there a degree 10 ideal solution yet?
Regards,
Ian Barrodale

Subject: Re: Great Progress on the Prouhet-Tarry-Escott problem!
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

Subject: Re: Great Progress on the Prouhet-Tarry-Escott problem!
Date: Wed, 08 Sep 1999 07:40:05 -0400
From: Steven Finch
To: jmchen@pub.jiangmen.gd.cn
Dear Chen Shuwen,
Congratulations!
Steve Finch

Subject: Re: Great Progress on the Prouhet-Tarry-Escott problem!
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

Subject: Re: Great Progress on the Prouhet-Tarry-Escott problem!
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

Subject: Re: Great Progress on the Prouhet-Tarry-Escott problem!
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

Subject: Re: Great Progress on the Prouhet-Tarry-Escott problem!
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,
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

Subject: Tarry-Escott-Prouhet
• 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

Keith Matthews ( krm@maths.uq.oz.au )
Date: Sun, 29 Jun 1997 12:45:40 +1000

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.
Date: Sun, 29 Jun 1997 00:02:38 -0700 (PDT)

Kevin Brown ( ksbrown@seanet.com )
Date: Sun, 29 Jun 1997 09:20:06 -0700 (PDT)

Earl D. Fife ( fife@calvin.edu )
Date: Tue, 1 Jul 1997 16:01:41 -0400

Joseph H. Silverman ( jhs@math.brown.edu )
I looked at your "sums of equal powers" pages and found them very interesting.
Date: Thu, 3 Jul 1997 10:04:13 -0400

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.
Date: Sat, 5 Jul 1997 07:58:59 -0700 (PDT)

Aleksandrs Mihailovs ( mihailov@math.upenn.edu )
Indeed, your page is extremely interesting.
Date: Sat, 5 Jul 1997 15:15:37 -0700

Aleksandrs Mihailovs ( mihailov@math.upenn.edu )
Date: Sat, 5 Jul 1997 18:50:07 -0700

Steven Finch ( sfinch@mathsoft.com )
Date: Sun, 06 Jul 1997 08:09:49 -0400

Giuseppe Melfi ( melfi@dm.unipi.it )
Very many thanks for your interesting site.
Date: Mon, 07 Jul 1997 10:20:57 +0200 (MET DST)

Eric W. Weisstein ( eww6n@carina.astro.virginia.edu )
Date: Mon, 7 Jul 1997 08:50:45 -0400 (EDT)

Lev Vsevolod ( seva@math.tau.ac.il )
I discovered your page a few days before. It looks exciting, though not quite in my line.
Date: Tue, 8 Jul 1997 17:36:21 +0300 (GMT+0300)

Josef Eschgfaeller ( esg@felix.unife.it )
Date: Tue, 8 Jul 1997 22:08:46 +0000 (GMT)

Mark Sheingorn ( marksh@panix.com )
Excellent page!! I very much enjoyed your homepage.
Date: Tue, 08 Jul 1997 21:39:27 +0000

Kevin Brown ( ksbrown@seanet.com )
Date: Wed, 9 Jul 1997 19:49:08 -0700 (PDT)

Joseph H. Silverman ( jhs@math.brown.edu )
I certainly think it is a very interesting problem, and the examples you have found are quite beautiful.
Date: Thu, 10 Jul 1997 07:59:18 -0400

Li Guo ( liguo@andromeda.rutgers.edu )
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.
Date: Thu, 10 Jul 1997 09:33:30 -0400 (EDT)

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.
Date: Thu, 17 Jul 1997 12:41:21 +0100

Jun Xu ( junxu@cs.uh.edu )
Date: Thu, 17 Jul 1997 22:13:09 -0500 (CDT)

David M. Bressoud ( bressoud@macalester.edu )
It does appear that you have done some very interesting mathematics.
Date: Thu, 24 Jul 1997 10:34:17 -0600

Tom Verhoeff ( wstomv@win.tue.nl )
Date: Wed, 30 Jul 1997 14:22:38 +0200 (MET DST)

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.
Date: Wed, 30 Jul 1997 19:37:33 -0400

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.
Thu, 31 Jul 1997 11:01:39 +0400 (EET DST)

Chandan Reddy ( creddy@husc.harvard.edu )
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.
Date: Fri, 1 Aug 1997 12:14:32 -0400 (EDT)
Ren Yuanhua ( gzjixin@public1.guangzhou.gd.cn )
The new version of Equal sums of like powers is quiet well. I read it carefully. A very good job indeed.
Date: Fri, 29 Aug 1997 17:25:28 +0800

Oktay Haracci ( oktayharacci@usa.net )
Date: Sun, 19 Oct 1997 14:58:15 +0400

Haracci (from Time Traveler Org. ) ( timeparadox@usa.net )
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)
Date: Sun Jan 18 01:52

Alec Mihailovs ( mihailov@math.upenn.edu )
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.
Date: Mon Jan 19 20:29

Richard Walker ( rcw9@tutor.open.ac.uk )
Congratulations on your very interesting pages and the many beautiful results you present.
Date: Thu, 19 Feb 1998 04:19:04 +0000

Last revised May 6, 2001.