A solution of a most difficult problem, in which the two forms aaxx+bbyy and aayy+bbxx must be rendered into squares
Euler first finds three families of particular solutions to the problem, then proceeds to a general solution. Finally, he extends the problem to finding a, b, c, and d that make all of the following three expressions into squares: aabb+ccdd, aacc+bbdd, aadd+bbcc.
Original Source Citation
Mémoires de l'académie des sciences de St.-Petersbourg, Volume 11, pp. 12-30.
Opera Omnia Citation
Series 1, Volume 5, pp.94-115.