Fermat and Wilson quotients for $p$-adic integers
Communications in Mathematics, Tome 6 (1998) no. 1, pp. 167-181 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 11A07, 11B68, 11S80
@article{COMIM_1998_6_1_a20,
     author = {Skula, Ladislav},
     title = {Fermat and {Wilson} quotients for $p$-adic integers},
     journal = {Communications in Mathematics},
     pages = {167--181},
     year = {1998},
     volume = {6},
     number = {1},
     mrnumber = {1822528},
     zbl = {1025.11001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_1998_6_1_a20/}
}
TY  - JOUR
AU  - Skula, Ladislav
TI  - Fermat and Wilson quotients for $p$-adic integers
JO  - Communications in Mathematics
PY  - 1998
SP  - 167
EP  - 181
VL  - 6
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/COMIM_1998_6_1_a20/
LA  - en
ID  - COMIM_1998_6_1_a20
ER  - 
%0 Journal Article
%A Skula, Ladislav
%T Fermat and Wilson quotients for $p$-adic integers
%J Communications in Mathematics
%D 1998
%P 167-181
%V 6
%N 1
%U http://geodesic.mathdoc.fr/item/COMIM_1998_6_1_a20/
%G en
%F COMIM_1998_6_1_a20
Skula, Ladislav. Fermat and Wilson quotients for $p$-adic integers. Communications in Mathematics, Tome 6 (1998) no. 1, pp. 167-181. http://geodesic.mathdoc.fr/item/COMIM_1998_6_1_a20/

[ADSl] T. Agoh K. Dilcher, and L. Skula: Fermat quotients for composite moduli. J. Number Theory 66 (1997), 29-50. | DOI | MR

[ADS2] T. Agoh K. Dilcher, and L. Skula: Wilson quotients for composite moduli. Math. Comp. 67, No. 222 (1998), 843-861. | DOI | MR

[BS] Z. I. Borevich I. R. Shafarevich: Number Theory. Academic Press, Orlando, 1966. | MR

[E] G. Eisenstein: Eine neue Gattung zahlentheoretischer Funktionen, welche von zwei Elementen abhängen und durch gewisse lineare Funktional-Gleichungen definiert werden. Bericht über die zur Bekanntmachung geeigenten Verhandlungen der Königl. Preuss. Akademie der Wissenschaften zu Berlin (1850), 36-42 (p.41). "Math. Werke, Gotthold Eisenstein", Band II, Chelsea, New York, 2nd ed. 1989, 705-711 (p. 7-10).

[FT] A. Friedmann J. Tamarkine: Quelques formules concernant la théorie de la fonction [x] et des nombres de Bernoulli. J. Reine Angew. Math. 135 (1909), 146-156.

[K] H. Koch: Galoissche Theorie der p-Erweiterungen. Berlin 1970. | MR | Zbl

[Lp] H.-W. Leopoldt: Zur Approximation des p-adischen Logarithmus. Abh. Math. Sem, Univ. Hamburg 25 (1961), 77-81. | DOI | MR | Zbl

[Lr1] M. Lerch: Zur Theorie des Fermatschen Quotienten $(a^{p-1} - 1)/p = q(a)$. Math. Ann. 60 (1905), 471-490. | DOI | MR

[Lr2] M. Lerch: Sur les théorèmes de Sylvester concernant le quotient de Fermat. C. R. Acad. Sci. Paris 142 (1906), 35-38.

[W] L. C. Washington: Introduction to Cyclotomic Fields. Second Edition, Springer, 1997. | MR | Zbl