E739 -- Regula facilis problemata Diophantea per numeros integros expedite resolvendi

(An easy rule for Diophantine problems which are to be resolved quickly by integral numbers)


Euler returns to the problem of making formulas of the form axx + bx + g into squares. He generalizes to try to find a and b solving axx + bx + g = zyy + hy + t. Again, it seems to rely on an initial solution and a clever application of solutions to Pellís equation. He does some nice examples: According to the records, it was presented to the St. Petersburg Academy on May 4, 1778.

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