English Title

Resolutio formulae diophanteae ab(maa+nbb) = cd(mcc+ndd) per numeros rationales

Authors

Leonhard Euler

Enestrom Number

716

Fuss Index

54

Original Language

Latin

Published as

Journal article

Published Date

1802

Written Date

1778

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.)

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

Included in

Mathematics Commons

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