In his magnificent book Number Theory: An approach through history, from Hammurapi to Legendre, André Weil quotes the article Solution de quelques questions d'analyse indéterminée, by L. Aubry (Sphinx-Œdipe, 7e année (1912), pp. 81–84). Can someone tell me something about this author? Or where to find a copy of that article? From what I was able to find online, it seems that all other (few) authors who quote this article are only aware of what André Weil wrote about it.

Edit: It turns out that Aubry's article had already been quoted by J. W. S. Cassels, in his 1978 book Rational quadratic forms.


L. Aubry was a French mathematician (most likely a high school teacher) who published 56 papers in mathematical journals and 4 books in the period 1894-1933, (according to Zentralblatt database). The paper you mention is not in this database. Most of his papers are in elementary mathematics journals for school children and amateurs. Such journals are rarely included in mathematics databases.

I also found references on this particular journal on Internet: https://www.amazon.fr/Sphinx-Oedipe-journal-mensuel-curiosit%C3%A9-concours/dp/B001C92HGI

It seems that it was published only for 7 years. If I really needed it, I would search in big French libraries. It is highly unlikely that this kind of journal has been digitalized. For example, this library seems to have it, and I would try Interlibrary loan (ILL):


Here is a Word Catalog entry:


If you have access to a scientific library, these data are sufficient for ordering it through the ILL.

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    $\begingroup$ According to this slide deck, Sphinx-Oedipe was edited by André Gérardin, and available volumes (in the BNF?) are 1906-1914, 1916-1917, 1920-1926, 1928. Reference is made to "L. Aubry, viticulteur à Jouy-les-Reims". $\endgroup$ – njuffa Dec 10 '18 at 20:36
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    $\begingroup$ This overview describes L. Aubry as an amateur mathematician, which jibes with the description as a winegrower in the slide deck (there is a champagne producer L. Aubry Fils in Jouy-les-Reims today): "the result goes back to a 1912 paper of the amateur mathematician L. Aubry" $\endgroup$ – njuffa Dec 10 '18 at 21:16
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    $\begingroup$ L. Aubry gave notice of his result in L'Intermédiaire des mathématiciens. Tome XIX, 1912, p. 177: "Tout nombre décomposable en trois carrés fractionnaires est décomposable en trois carrés entiers. J'ai donné une démonstration directe et très élémentaire de cette proposition, dans Sphinx-Œdipe (1912, p. 81). L. Aubry" $\endgroup$ – njuffa Dec 10 '18 at 21:43
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    $\begingroup$ His first name is definitely Léon. Based on p. 55 here, I believe his full name is probably Léon Jean Reginald Aubry, although I have not been able to get any independent evidence that either of these middle names is correct for the person @José Carlos Santos is interested in. (continued) $\endgroup$ – Dave L Renfro Dec 11 '18 at 14:17
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    $\begingroup$ I thought the 1895-1923 years were for when he taught at the high school, since the years are next to that and not his name. It is also reasonably consistent that someone born in 1868 would begin teaching high school in 1895. However, as I said, I don't have any independent evidence to connect the L. Aubry with the middle names given on p. 55, nor any independent evidence to connect either with the 1868-1931 person. $\endgroup$ – Dave L Renfro Dec 11 '18 at 15:10

Sphinx-Œdipe was a publication edited by the French mathematician André Gérardin, as noted in this recent report: Maarten Bullynck, "From exploration to theory-driven tables (and back again). A History of Tables in Number Theory.":

Between 1906 and 1928 Gérardin published a special journal, Sphinx-Oedipe, journal mensuel de la curiosité et de concours

In 2017, a lecturer at the University of Nantes in France gave a talk on this journal and its editor:

Jenny Boucard. "André Gérardin (1879-1953) et la revue Sphinx-Oedipe (1906-19??)". 2017. Intervention dans le cadre d'une table ronde sur le thème "Les Journaux mathématiques au XXe siècle" (ANR Cirmath) (Paris, France)

The slides from the talk are available here and here.

Boucard notes that library holdings of the publication are incomplete and tracked down the following volumes of Sphinx-Œdipe: 1906-1914, 1916-1917, 1920-1926, 1928. It is unclear whether the listed volumes are all available from the BNF (Bibliothèque nationale de France).

Boucard notes that the publication used contributions from a mix of both regional and international authors, and gives the following examples of regional contributors:

L. Chanzy, professeur de lycée à Nancy ou L. Aubry, viticulteur à Jouy-les-Reims

In English: "L. Chanzy, high school teacher in Nancy or L. Aubry, winegrower in Jouy-les-Reims". The description of L. Aubry as a "viticulteur", i.e. a winegrower, seems plausible, as there is a champagne producer L. Aubry Fils (English: L. Aubry Son) in Jouy-les-Reims today.

A paper by Pete L. Clark, "Quadratic Forms Over Global Fields", describes L. Aubry as an amateur mathematician:

[...] the result goes back to a 1912 paper of the amateur mathematician L. Aubry

L. Aubry's first name was Léon, as can be seen from these 1911 proceedings:

Les travaux de la Section de Mathématiques et d'Astronomie de l'Association Française pour l'Avancement des Sciences. Congrès de Dijon, 31 juillet-5 août 1911. [...]
M. Léon Aubry, de Jouy-les-Reims, adresse deux mémoires intitulés Sur les diviseurs des formes quadratiques et Démonstration du théorème de Bachet

Also, in this 1924 conference program:

Les Mathématiques à l'Association française pour l'Avancement des Sciences, Congrès des Grenoble. Juillet 1925 [...]
Léon AUBRY, Jouy-les-Reims: Sur la congruence $$\frac{(x + \sqrt{k})^{n} - (x -\sqrt{k})^n}{2\sqrt{k}}\equiv 0\;\;\;\; (\mathrm{mod.}\;p)$$

L. Aubry also made note of the result referenced in the question in L'Intermédiaire des mathématiciens. Tome XIX, Paris 1912, p. 177:

Tout nombre décomposable en trois carrés fractionnaires est décomposable en trois carrés entiers. J'ai donné une démonstration directe et très élémentaire de cette proposition, dans Sphinx-Œdipe (1912, p. 81). L. Aubry

In English: "Any number decomposable into three fractional squares is decomposable into three whole squares. I gave a direct and very basic demonstration of this proposition, in Sphinx-Oedipe (1912, p. 81)"

  • $\begingroup$ Thank you. Meanwhile, I had already found part of what you wrote in your answer. I sent an e-mail to Jenny Boucard asking her whether she is able to get me a copy of Aubry's article. $\endgroup$ – José Carlos Santos Dec 11 '18 at 22:54

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