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 Pellís 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.

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