An investigation of two numbers of the form xy(x4–y4), of which the product and the quotient will be a square
In Volume XV of the Novi Commentarii, Euler found integers x, y, z such that xy±z(x+y) and xy±z(x−y) are all squares. In this paper, he describes a more elegant solution, which first requires one to determine when xy(x4−y4) is a square. Then, given an initial solution, he uses a double-quadratic technique to find a chain of solutions.
Original Source Citation
Mémoires de l'académie des sciences de St.-Petersbourg, Volume 11, pp. 31-45.
Opera Omnia Citation
Series 1, Volume 5, pp.116-130.