Talk:Sum of four cubes problem

More recent references

Possibly relevant:

Brüdern, Jörg and Watt, Nigel, On Waring's problem for four cubes. Duke Math. J. 77 (1995), no. 3, 583–606. [1]
Koichi Kawada, On the sum of four cubes, Mathematika , Volume 43 , Issue 2 , December 1996 , pp. 323 - 348, [2]
Guy, R. K. ``Sum of Four Cubes. §D5 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 151-152, 1994.
These slides by Andrew Sutherland attribute this problem to Sierpinski.

--JBL (talk) 16:09, 3 April 2022 (UTC)[reply]

Rational integer

If anyone disagrees with my last edit then please put “rational numbers” instead. “Rational integers” is redundant. Thx-Singer ArtfulSinger95 (talk) 17:39, 7 September 2022 (UTC)[reply]

"Ratioal integer" is correct and less ambiguous than "integer", since there are algebraic integers which are not rational numbers. By the way, I think that "rational number", here, would be a misrepresentation of the problem. Marvoir (talk) 09:02, 21 September 2022 (UTC)[reply]

It is only ambiguous in a context in which some other kind of integer (Gaussian integers, algebraic integers, ...) are discussed. That is not the case here. JBL (talk) 17:10, 21 September 2022 (UTC)[reply]

See here, p. 20 : Bourbaki defines "rational integers" in a context where no other "integer" appears. Marvoir (talk) 17:20, 21 September 2022 (UTC)[reply]

I have three responses to this: (1) In fact, that book does discuss "complex integers" and "algebraic integers" (beginning on page 661). (2) In the vast majority of uses of "integer" in that book, it is unmodified; this is a good piece of evidence that there is not any true ambiguity here. (3) Bourbaki is a terrible model for how one should write a general-purpose encyclopedia; the topic of this article is understandable by bright middle school students, and we should aspire to have the article also be so comprehensible. --JBL (talk) 17:41, 21 September 2022 (UTC)[reply]

OK, let it be. Marvoir (talk) 08:04, 22 September 2022 (UTC)[reply]

Source of 5 identities

After reading of Demjanenko's paper, I couldn't find the identities dealing with easier cases (6k, 6k+3, 18k+1, 18k+7, and 18k+8). Assuming I understood correctly, Demjanenko splitted case 18k+2 into 4 (easily demonstradeble part)+1 (harder to deal with) subcases. And to answer 18k-2, Demjanenko used 18k+2 and applied identity which allows change signs. So this leads to a question where the first 5 identities come from. Revoy attributes them to Mordel(1968) which seems unplausible because Demjanenko's article was published in 1966. Unfortunately, my French is lacking so couldn't quite understand why Revoy spent so much time on 18k+2. Revoy also references that there are no easy identities for 9k+-4. 213.226.141.200 (talk) 20:14, 17 May 2023 (UTC)[reply]

Some of those 5 identities are given in the 1959 Sierpiński and Schinzel paper, description of which I've added to the article. That paper covers all the same categories of numbers as those identities, even though some of the identities themselves are different -- so it is entirely plausible that Mordel found simpler identities to replace the more complex ones given by Sierpiński and Schinzel.

I only found those 5 in the 2004 paper by Cohen (which isn't just a translation of Demjanenko's paper, even though it doesn't cite any other sources), so that's what I referenced, not as the original source of those 5 but as a place where they can be found. If someone can verify that Mordel gave those 5 decades earlier, we could update that section to cite Mordel instead of Cohen. (Or maybe at least Revoy.) Zacronos2 (talk) 22:51, 15 January 2026 (UTC)[reply]