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)
Euler wants to find a and b such that the following four quantities are all squares: ab+a+b, ab+a-b, ab-a+b, and ab-a-b.
to the records, it was presented to the St. Petersburg Academy on March 5, 1770.
Originally published in Novi Commentarii academiae scientiarum Petropolitanae 15, 1771, pp. 29-50
Opera Omnia: Series 1, Volume 3, pp. 148 - 171
- Reprinted in Commentat. arithm. 1, 1849, pp. 414-426 [E405a]
- A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
- Original Publication: E405
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