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)
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.
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.
- A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
- Original Publication: E523
- English Translation (Mark Snavely and Phil Woodruff): E523
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