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)


Summary:

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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