Talk:Prouhet–Tarry–Escott problem

Magic squares

Have you noticed the relation to the 3x3 magic square ${\begin{matrix}4&9&2\\3&5&7\\8&1&6\end{matrix}}$ ? Could you give a reference (who found this first and where), please? 62.218.164.30 (talk) 18:31, 12 April 2008 (UTC)

Example

Recently an anonymous editor changed the main example from {492, 276, 618, 834} and {294, 438, 816, 672} with n=3 to { 0,5,6,16,17,22 } and { 1,2,10,12,20,21 } with n=5. I like that the new example has smaller elements, and so is easier to verify manually, and that is has a larger n. But I don't like that it includes 0. Does anyone else have any feelings about this? -- Dominus (talk) 13:23, 14 August 2008 (UTC)

If you don't like the zero you can add one to all the numbers to get a solution with no zero. Weburbia (talk) 17:13, 31 January 2018 (UTC)

Disjoint?

The article now says:

the Prouhet-Tarry-Escott problem asks for two distinct sets A and B of n integers each, such that:

$\sum _{a\in A}a^{i}=\sum _{b\in B}b^{i}$

for each integer i from 1 to a given k.

If any number were in both sets, A and B, then one could subtract the corresponding terms from both sides and equality would still hold. Therefore no generality would be lost by saying "two disjoint sets" instead of just "two distinct sets". It seems to me it would be clearer if one required disjointness. Michael Hardy (talk) 16:33, 16 June 2009 (UTC)

Now I've changed it and explained in the edit summary. Michael Hardy (talk) 20:30, 16 June 2009 (UTC)

What is the statement of the problem?

Dear Dominus! In mathematics, a problem/conjecture is usually a definite statement, something that can either be true or false, something with a yes/no answer. That's why I corrected the lede, stating the conjecture, to a statement like "for every n there is a...". In the current form it is unclear what the problem requires: one example for one n, infinitely many examples for one n, infinitely many examples for infinitely many n, examples for all n. But then, in this loose form, the problem is unsolvable, nobody knows what is required for a solution.That is not what we usually have with mathematical problems, don't we? Kope (talk) 05:03, 27 June 2009 (UTC)