E405  Solutio problematis, quo duo quaeruntur numeri, quorum productum tam summa quam differentia eorum sive auctum sive minutum fiat quadratum
(A solution of a problem about two numbers which are searched for, of which their product, increased or decreased by their sum or difference, will be a square)
Summary:
Euler wants to find a and b such that the following four quantities are all squares: ab+a+b, ab+ab, aba+b, and abab.
According
to the records, it was presented to the St. Petersburg Academy on March 5, 1770.
Publication:

Originally published in Novi Commentarii academiae scientiarum Petropolitanae 15, 1771, pp. 2950

Opera Omnia: Series 1, Volume 3, pp. 148  171
 Reprinted in Commentat. arithm. 1, 1849, pp. 414426 [E405a]
 A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
Documents Available:
 Original Publication: E405
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