E773 -- Solutio problematis difficillimi, quo hae duae formulae aaxx + bbyy et aayy + bbxx quadrata reddi debent

(A solution of a most difficult problem, in which the two forms aaxx + bbyy et aayy + bbxx must be rendered into squares)


Euler first finds three families of particular solutions, then proceeds to a general solution. Finally, he extends the problem to finding a, b, c, and d that make the following three expressions all squares: aabb + ccdd, aacc + bbdd, aadd + bbcc.

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