On a singular type of Diophantine questions and a most recondite method by which they are to be resolved
First, Euler notices that if N has the form aa+nbb, then Nλ also has that form. He demonstrates how to determine the forms with a few examples. Then he poses the general problem for N = aa+nbb: to find the powers of N that make Nλ = xx+n, and, in general, how to minimize the value of y in a value xx+nyy.
Original Source Citation
Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 9, pp. 3-18.
Opera Omnia Citation
Series 1, Volume 4, pp.221-234.