E279  De resolutione formularum quadricarum indeterminatarum per numeros integros
(On the resolution of formulas of squares of indeterminates by integral numbers)
Summary:
In this paper, Euler returns to the problem axx + bx + c = yy, first approached in E29, and uses the tools of Pell’s equation. He also begins to find some of the properties of quadratic reciprocity. On the last page, he uses the term "Theory of Numbers," possibly the first use of this term.
According
to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy on September 21,
1758.
According to the records, it was presented to the St. Petersburg Academy on October 15,
1759.
Publication:

Originally published in Novi Commentarii academiae scientiarum Petropolitanae 9, 1764, pp. 339

Opera Omnia: Series 1, Volume 2, pp. 576  611
 A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
 Reprinted in Commentat. arithm. 1, 1849, pp. 297315 [E279a]
Documents Available:
 Original publication: E279
 Other works that cite this paper include:
 Andre Weil, Number Theory
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