MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

A "not well understood" proof, do you know if one knows by now the conceptual background?:

share|cite|improve this question
up vote 3 down vote accepted

There is a paper by Philippe Revoy that analyses and expands on this result.

Its abstract reads (the paper itself is in French):

In this note, we do a systematic study of first degree identities $\sum_{i=1}^4 P_i(x)^3 = P x + q$, $P_i \in \mathbb{Z}[x]$, occuring in the four cube problem over $\mathbb{Z}$; we try to explain the difficulties to get identities for numbers $18k + 2$ which were found by Demjanenko and we show we can get a lot of similar identities, so that most integers of that residue class are sum of four cubes unless they are divisible by certain prime numbers, possibly an infinity, and we settle the question using second degree identities.

The paper itself seems to be freely available on, the link below should take you there directly:

Ph. Revoy, Sur les sommes de quatre cubes, Enseign. Math 29 (1983), 209-220

share|cite|improve this answer
Thanks for that quick reaction, quid! – Thomas Riepe Jul 24 '13 at 21:25
You are welcome! – user9072 Jul 24 '13 at 21:26

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.