Proof of a theorem of Fermat that every number whether whole or fraction is the sum of four or fewer squares
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 Fp. 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.
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 5, pp. 13-58.
Opera Omnia Citation
Series 1, Volume 2, pp.338-372.