On the resolution of formulas of squares of indeterminates by integral numbers
According to Jacobi, a treatise with this title was read to the Berlin Academy on September 21, 1758. According to St. Petersburg Academy records, it was presented to that Academy on October 15, 1759.
In this paper, Euler returns to the equation axx+bx+c = yy, first approached in E29, and uses the tools of Pell's equation. He also discovers some of the properties of quadratic reciprocity. On the last page, he uses the phrase "Theory of Numbers," possibly the first use of this term.
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 9, pp. 3-39.
Opera Omnia Citation
Series 1, Volume 2, pp.576-611.