Demonstratio theorematis Fermatiani omnem numerum sive integrum sive fractum esse summam quatuor pauciorumve quadratorum

English Title

Proof of a theorem of Fermat that every number whether whole or fraction is the sum of four or fewer squares

Authors

Leonhard Euler

Enestrom Number

242

Original Language

Latin

Content Summary

This paper contains the beginnings of group theory, showing in particular that quadratic residues of a prime p form a subgroup of index 2 of the multiplicative group F_p. Euler ends up with a result about rational squares rather than integer squares, so it falls just short of its mark. Since there is no title page for this paper, Eneström suggests that it is a only a continuation of E241.

Published as

Journal article

Published Date

1760

Written Date

1751

Original Source Citation

Novi Commentarii academiae scientiarum Petropolitanae, Volume 5, pp. 13-58.

Opera Omnia Citation

Series 1, Volume 2, pp.338-372.

Record Created

2018-09-25