Here's what we have so far: ---------------------------------------------------------------------------- 6 1 8 4 9 2 7 5 3 <-> 3 5 7 2 9 4 8 1 6 ---------------------------------------------------------------------------- 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.[1] ----------------------------------------------------------------------------- 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.[2] ----------------------------------------------------------------------------- References: [1] R. Holmes, The Magic Magic Square, The Mathematical Gazette, December 1970, p.376 [2] ? ---------------------------------------------------------------------------- The Lo Shu is more "magical" than most of us have known for thousands of years! Paul --- Richard Guy <rkg@cpsc.ucalgary.ca> wrote:

Ditto. R.

---------- Forwarded message ---------- Date: Sat, 12 Apr 2008 09:23:06 +0200 From: Christian Boyer <cboyer@club-internet.fr> Reply-To: math-fun <math-fun@mailman.xmission.com> To: 'math-fun' <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Prouhet-Tarry-Escott in Magic Square

Same properties on:

...

...

816^3 + 672^3.

...

...

816^2 + 672^2 492^3 + 276^3 + 618^3 + 834^3 = 294^3 + 438^3

...

...

816^1 + 672^1 492^2 + 276^2 + 618^2 + 834^2 = 294^2 + 438^2

...

...

492^1 + 276^1 + 618^1 + 834^1 = 294^1 + 438^1

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.

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