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

Published as

Collection article

Published Date

1862

Written Date

1772

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."

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

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