English Title

On the criteria of whether equation fxx + gyy = hz2 admits a resolution or not

Authors

Leonhard Euler

Enestrom Number

556

Fuss Index

70

Original Language

Latin

Content Summary

Euler's motivating example is that xx+yy = 2zz has solutions but that xx+yy = 3zz has no solutions. The question is, for what values of f, g and h will fxx+gyy = hzz have solutions? He shows that, given single values for f and g and three values of h for which there are solutions, one may construct a fourth value for h, and calls it (section 12) a "most elegant theorem."

Published as

Collection article

Published Date

1862

Written Date

1772

Original Source Citation

Opuscula analytica, Volume 1, pp. 211-241.

Opera Omnia Citation

Series 1, Volume 4, pp.1-24.

Record Created

2018-09-25

Included in

Mathematics Commons

Share

COinS