E262 -- Theoremata circa residua ex divisione potestatum relicta
(Theorems on residues obtained by the division of powers)
Summary:
This paper contains theorems about power residues mod a prime, among them the
theorems that they don’t repeat, a multiplicative homomorphism property, and a
solvability property. This paper shows insight into the properties of groups.
According
to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy on February 13, 1755.
Publication:
-
Originally published in Novi Commentarii academiae scientiarum Petropolitanae 7, 1761, pp. 49-82
-
Opera Omnia: Series 1, Volume 2, pp. 493 - 518
- Reprinted in Commentat. arithm. 1, 1849, pp. 260-273 [E262a]
- A translation of selections of E262 is published in D. J. Struik's
A Source Book in Mathematics, 1200-1800 (1969, Harvard University Press), pp. 31-35.
- According to Eneström,
A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
Documents Available:
- Original publication: E262
- English Translation (Jordan Bell): E262
Return to the Euler Archive