E523 -- De tribus numeris quadratis, quorum tam summa quam summa productorum ex binis sit quadratum
(On three square numbers, of which the sum and the sum of products two apiece will be a square)
Summary:
Euler wants xx + yy + zz and xxyy + xxzz + yyzz both to be squares.
According to the
records, it was presented to the St. Petersburg Academy on September 7, 1780.
Publication:
-
Originally published in Acta Academiae Scientarum Imperialis Petropolitinae 1779, 1782, pp. 30-39
-
Opera Omnia: Series 1, Volume 3, pp. 453 - 462
- Reprinted in Commentat. arithm. 2, 1849, pp. 457-461 (The treatise by J. A. Euler is printed on pp.
462-466) [E523a]
- A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
Documents Available:
- Original Publication: E523
- English Translation (Mark Snavely and Phil Woodruff): E523
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