Theorems on residues obtained by the division of powers
| dc.creator | Euler, Leonhard | |
| dc.date | 2006-08-18 | |
| dc.date | 2007-08-05 | |
| dc.date.accessioned | 2026-07-07T08:22:09Z | |
| dc.date.available | 2026-07-07T08:22:09Z | |
| dc.description | This is an English translation of Euler's ``Theoremata circa residua ex divisione potestatum relicta'', Novi Commentarii academiae scientiarum Petropolitanae 7 (1761), 49-82. E262 in the Enestrom index. Euler gives many elementary results on power residues modulo a prime number p. He shows that the order of a subgroup generated by an element a in F_p^* must divide the order p-1 of F_p^* (i.e. a special case of Lagrange's theorem for cyclic groups). Euler also gives a proof of Fermat's little theorem, that a^{p-1} = 1 mod p for a relatively prime to p (i.e. not 0 mod p). He remarks that this proof is more natural, as it uses multiplicative properties of F_p^* instead of the binomial expansion. Thanks to Jean-Marie Bois for pointing out some typos. | |
| dc.description | 27 pages, E262 | |
| dc.identifier | https://arxiv.org/abs/math/0608467 | |
| dc.identifier | http://arxiv.org/abs/math/0608467 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135556 | |
| dc.subject | History and Overview | |
| dc.subject | Number Theory | |
| dc.subject | 01A50, 11A15 | |
| dc.title | Theorems on residues obtained by the division of powers | |
| dc.type | text |