## E452 -- Resolutio aequationis $$Ax^2 + 2Bxy + Cy^2 + 2Dx + 2Ey + F = 0$$ per numeros tam rationales quam integros

(The resolution of the equation $$Ax^2 + 2Bxy + Cy^2 + 2Dx + 2Ey + F = 0$$ by rational and integral numbers)

Summary:

This is another paper on extending a known solution to the equation to find new solutions.

According to the records, it was presented to the St. Petersburg Academy on November 19, 1772.

Publication:
• Originally published in Novi Commentarii academiae scientiarum Petropolitanae 18, 1774, pp. 185-197
• Opera Omnia: Series 1, Volume 3, pp. 297 - 309
• Reprinted in Commentat. arithm. 1, 1849, pp. 549-555 [E452a]
Documents Available:
• Original Publication: E452
• Other works that cite this paper include:
• Andre Weil, Number Theory