Already seen these formulas, but I can't remember where. Joshua, I have the paper of Burchnall-Chaundy, it does not contain these formulas. Here are some other nice formulas by R. Holmes, The Magic Magic Square, The Mathematical Gazette, December 1970, p.376: 6 1 8 7 5 3 2 9 4 618^n + 753^n + 294^n = 816^n + 357^n + 492^n (rows) 672^n + 159^n + 834^n = 276^n + 951^n + 438^n (columns) 654^n + 132^n + 879^n = 456^n + 231^n + 978^n (diagonals \) 852^n + 174^n + 639^n = 258^n + 471^n + 936^n (diagonals /) True for n = 1 and 2. True again if you delete the first digit in each number. True again if you delete the second digit in each number. True again if you delete the last digit in each number. Christian. -----Message d'origine----- De : math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] De la part de Joshua Zucker Envoyé : samedi 12 avril 2008 00:48 À : math-fun Objet : Re: [math-fun] Prouhet-Tarry-Escott in Magic Square On Fri, Apr 11, 2008 at 2:56 PM, Richard Guy <rkg@cpsc.ucalgary.ca> wrote:
On Fri, 11 Apr 2008, Paul Muljadi wrote:
Tarry-Escott solution: 492^1 + 276^1 + 618^1 + 834^1 = 294^1 + 438^1 + 816^1 + 672^1 492^2 + 276^2 + 618^2 + 834^2 = 294^2 + 438^2 + 816^2 + 672^2 492^3 + 276^3 + 618^3 + 834^3 = 294^3 + 438^3 + 816^3 + 672^3.
Wikipedia has it but with no citation; Mathworld doesn't have it. J.L.Burchnall & T.W.Chaundy, A type of "Magic Square" in Tarry's problem,Quart. J. Math., 8(1937), 119-130 looks promising, but I don't have that journal; if you have the right kind of subscription you can find it at http://qjmath.oxfordjournals.org/content/volos-8/issue1/index.dtl and see if it does indeed contain this fact. That's about all I could find ... the other 1937 articles on the Tarry-Escott problem seem to cite this one but they don't have this result. --Joshua Zucker