English Title
Resolutio formulae diophanteae ab(maa+nbb) = cd(mcc+ndd) per numeros rationales
Enestrom Number
716
Fuss Index
54
Original Language
Latin
Content Summary
In a previous paper, Euler solved A4 + B4 = C4 + D4 by reducing that problem to solving ab(aa + bb) = cd(cc + dd) in integers. 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 Euler makes the conjecture that two cubes can't sum to a cube, three fourth powers can't sum to a 4th power, and, in general, the sum of n–1 nth powers can't be an nth power. (This conjecture has since been shown to be false.)
Published as
Journal article
Published Date
1802
Written Date
1778
Original Source Citation
Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 13, pp. 45-63.
Opera Omnia Citation
Series 1, Volume 4, pp.329-351.
Record Created
2018-09-25
E716en.pdf (641 kB)
E716en.pdf (641 kB)
