English Title

On a singular type of Diophantine questions and a most recondite method by which they are to be resolved

Authors

Leonhard Euler

Enestrom Number

683

Fuss Index

76

Original Language

Latin

Published as

Journal article

Published Date

1795

Written Date

1777

Content Summary

First, Euler notices that if N has the form aa+nbb, then Nλ also has that form. He demonstrates how to determine the forms with a few examples. Then he poses the general problem for N = aa+nbb: to find the powers of N that make Nλ = xx+n, and, in general, how to minimize the value of y in a value xx+nyy.

Original Source Citation

Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 9, pp. 3-18.

Opera Omnia Citation

Series 1, Volume 4, pp.221-234.

Record Created

2018-09-25

Included in

Mathematics Commons

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