E683 -- De singulari genere quaestionum Diophantearum et methodo maxime recondita eas resolvendi

(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 is of the form aa + nbb, then Nl is also of that form. He demonstrates how to determine the forms with a few examples. Then he poses the general problem, N = aa + nbb, to find the powers of N that make Nl = xx + n, and, in general, how to minimize the value of y in a value xx + nyy.

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