E796 -- Recherches sur le problem de trois nombres carres tels que la somme de deux quelconques moins le troisieme fasse un nombre carre
(Research into the problem of three square numbers such that the sum of any two less the third one provides a square number)
In the first part, Euler presents several different methods of finding values of x, y, and z that make the
following three expressions all squares: yy + zz - xx, xx + zz - yy, xx + yy - zz.
In the second part, entitled "Solution díun probleme assez curieux savoir: trouver quatre nombres positifs et inegaux entr-eux
tels que la somme de deux soit toujours un carre," Euler presents several solutions, by familiar means.
The third part is entitled "Supplement au probleme de quatre nombres donít la somme de deux fassent toujours un nombre carre."
It was probably presented to the St.
Petersburg Academy on March 1, 1781.
Originally published in Commentationes arithmeticae 2, 1849, pp. 603-616
Opera Omnia: Series 1, Volume 5, pp. 303 - 329
- Reprinted in Sphinx-OEdipe (Nancy) , 1906/7, pp. 163-183 [E796b]
- Reprinted in Opera Postuma 1, 1862, pp. 105-118 [E796a]
- Original publication: E796
- A new translation of E796 has been prepared by Thomas Osler and Kristen McKeen. The translation is both faithful and highly readable, and is recommended.
- Osler and McKeen have also prepared a section-by-section Synopsis of E796. This is an excellent place to start for those looking for the main ideas this work.
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