E716 -- Resolutio formulae Diophanteae ab(maa + nbb) = cd(mcc + ndd) per numeros rationales

(The resolution of the Diophantine formula ab(maa+nbb) = cd(mcc+ndd) by rational numbers)


In solving A4 + B4 = C4 + D4, it was reduced to solving in integers ab(aa + bb) = cd(cc + dd). This paper generalizes that. It opens with a citation of Fermat's Last Theorem, with the remark that Fermat's proof has been lost. Then it makes the conjecture that two cubes can't sum to be a cube, three fourth powers a 4th power, or, in general, n - 1 sums of nth powers can't be an nth power. [This conjecture has been shown to be false.]

According to the records it was presented to the St. Petersburg Academy on December 17, 1778.

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