Pseudoprimes
Pokroky matematiky, fyziky a astronomie (2003)
- Volume: 48, Issue: 2, page 143-151
- ISSN: 0032-2423
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topKřížek, Michal, and Somer, Lawrence. "Pseudoprvočísla." Pokroky matematiky, fyziky a astronomie 48.2 (2003): 143-151. <http://eudml.org/doc/196855>.
@article{Křížek2003,
author = {Křížek, Michal, Somer, Lawrence},
journal = {Pokroky matematiky, fyziky a astronomie},
keywords = {Fermat theorem; prime; Carmichael number; Fermat theorem; prime; Carmichael number},
language = {cze},
number = {2},
pages = {143-151},
publisher = {Jednota českých matematiků a fyziků},
title = {Pseudoprvočísla},
url = {http://eudml.org/doc/196855},
volume = {48},
year = {2003},
}
TY - JOUR
AU - Křížek, Michal
AU - Somer, Lawrence
TI - Pseudoprvočísla
JO - Pokroky matematiky, fyziky a astronomie
PY - 2003
PB - Jednota českých matematiků a fyziků
VL - 48
IS - 2
SP - 143
EP - 151
LA - cze
KW - Fermat theorem; prime; Carmichael number; Fermat theorem; prime; Carmichael number
UR - http://eudml.org/doc/196855
ER -
References
top- Alford, W. R., Granville, A., Pomerance, C., 10.2307/2118576, Ann. of Math. 140 (1994), 703–722. (1994) Zbl0816.11005MR1283874DOI10.2307/2118576
- Baillie, R., Wagstaff, S. S., 10.1090/S0025-5718-1980-0583518-6, Math. Comp. 35 (1980), 1391–1417. (1980) Zbl0458.10003MR0583518DOI10.1090/S0025-5718-1980-0583518-6
- Banachiewicz, T., O związku pomiędzy pewnym twierdzeniem matematyków chińskich a formą Fermata na liczby pierwsze, Spraw. Tow. Nauk, Warszawa 2 (1909), 7–11. (1909)
- Beeger, N. G. W. H., 10.2307/2306320, Amer. Math. Monthly 58 (1951), 553–555. (1951) MR0043798DOI10.2307/2306320
- Carmichael, R. D., 10.1090/S0002-9904-1910-01892-9, Bull. Amer. Math. Soc. 16 (1910), 232–238. (1910) Zbl41.0226.04MR1558896DOI10.1090/S0002-9904-1910-01892-9
- Carmichael, R. D., 10.2307/2972687, Amer. Math. Monthly 19 (1912), 22–27. (1912) Zbl43.0276.17MR1517641DOI10.2307/2972687
- Cipolla, M., 10.1007/BF02419871, Annali di Matematica (3) 9 (1904), 139–160. (1904) DOI10.1007/BF02419871
- Dickson, L. E., History of the theory of numbers, vol. I, Divisibility and primality, Carnegie Inst., Washington 1919. (1919)
- Duparc, H. J. A., On Carmichael numbers, Poulet numbers, Mersenne numbers and Fermat numbers, Rapport ZW 1953-004, Math. Centrum Amsterdam 1953, 1–7. (1953) Zbl0053.02401MR0062143
- Erdős, P., 10.2307/2307640, Amer. Math. Monthly 57 (1950), 404–407. (1950) Zbl0038.18105MR0036259DOI10.2307/2307640
- Jarden, D., Existence of an infinitude of composite for which (Hebrew, Engl. Summary), Riveon Lematematika 4 (1950), 65–67. (1950) MR0038995
- Jeans, J. H., The converse of Fermat’s theorem, Messenger of Mathematics 27 (1897/98), 174. (1897) Zbl29.0151.02
- Joo, I., Phong, B. M., On super Lehmer pseudoprimes, Studia Sci. Math. Hungar. 25 (1990), 121–124. (1990) Zbl0615.10016MR1102204
- Kiss, E., 10.1006/hmat.1998.2212, Historia Math. 26 (1999), 68–76. (1999) Zbl0920.11001MR1677471DOI10.1006/hmat.1998.2212
- Kiss, P., Some results on Lucas pseudoprimes, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 28 (1985), 153–159. (1985) Zbl0613.10008MR0856986
- Korselt, A., Problème chinois, L’Interm. des Math. 6 (1899), 143. (1899)
- Křížek, M., Luca, F., Somer, L., 17 lectures on Fermat numbers: From number theory to geometry, CMS Books in Mathematics, vol. 9, Springer-Verlag, New York 2001. (2001) Zbl1010.11002MR1866957
- Lehmer, D. H., 10.2307/2301798, Amer. Math. Monthly 43 (1936), 346–354. (1936) Zbl0014.10204MR1523680DOI10.2307/2301798
- Mahnke, D., Leibniz auf der Suche nach einer allgemeinen Primzahlgleichung, Bibliotheca Math. 13 (1913), 29–61. (1913) Zbl43.0068.02
- Mąkowski, A., On a problem of Rotkiewicz on pseudoprime numbers, Elem. Math. 29 (1974), 13. (1974) Zbl0271.10010MR0335424
- Malo, E., Nombres qui sans être premiers, verifient exceptionnellement une congruence de Fermat, L’Interm. des Math. 10 (1903), 88. (1903)
- Phong, B. M., On super Lucas and super Lehmer pseudoprimes, Studia Sci. Math. Hungar. 23 (1988), 435–442. (1988) Zbl0597.10004MR0982690
- Pomerance, C., 10.1090/S0025-5718-1981-0628717-0, Math. Comp. 37 (1981), 587–593. (1981) Zbl0511.10002MR0628717DOI10.1090/S0025-5718-1981-0628717-0
- Pomerance, C., A new lower bound for the pseudoprime counting function, Illinois J. Math. 26 (1982), 4–9. (1982) Zbl0474.10035MR0638549
- Pomerance, C., Selfridge, J. L., Wagstaff, S. S., 10.1090/S0025-5718-1980-0572872-7, Math. Comp. 35 (1980), 1003–1026. (1980) MR0572872DOI10.1090/S0025-5718-1980-0572872-7
- Porubský, Š., Fermat a teorie čísel aneb Problematika dělitelů a dokonalá čísla, In: Matematik Pierre de Fermat (eds. A. Šolcová et al.), Cahiers du CEFRES 28 (2002), 49–86. (2002)
- Poulet, P., Table des nombres composés vérifiant le théeorème de Fermat pour le module jusqu’à , Sphinx 8 (1938), 42–52. Errata in Math. Comp. 25 (1971), 944–945, Math. Comp. 26 (1972), 814. (1938) Zbl64.0116.03MR0655816
- Ribenboim, P., The book of prime number records, Springer, New York 1988, 1989. (1988) Zbl0642.10001MR1016815
- Ribenboim, P., The new book of prime number records, Springer, New York 1996. (1996) Zbl0856.11001MR1377060
- Rotkiewicz, A., Sur les nombres pseudopremiers de la forme , C. R. Acad. Sci. Paris Sér. I Math. 257 (1963), 2601–2604. (1963) Zbl0116.03501MR0162757
- Rotkiewicz, A., Sur les formules donnant des nombres pseudopremiers, Colloq. Math. 12 (1964), 69–72. (1964) Zbl0129.02703MR0166138
- Rotkiewicz, A., On the pseudoprimes of the form , Proc. Cambridge Philos. Soc. 63 (1967), 389–392. (1967) Zbl0152.03102MR0209220
- Rotkiewicz, A., Pseudoprime numbers and their generalizations, Stud. Assoc. Fac. Sci. Univ. Novi Sad 1972. (1972) Zbl0324.10007MR0330034
- Rotkiewicz, A., Lucas and Frobenius pseudoprimes, Proc. of the 10th Internat. Conf. on Fibonacci Numbers and their Applications, Flagstaff, Arizona, 2002 (to appear in Kluwer), 1–21. (2002) MR2076674
- Sierpiński, W., Remarque sur une hypothèse des Chinois concernant les nombres , Colloq. Math. 1 (1948), 9. (1948) Zbl0037.30903MR0023256
- Somer, L., On Fermat -pseudoprimes, In: Théorie des nombres (éd. J.-M. De Koninck, C. Levesque), Walter de Gruyter, Berlin, New York, 1989, 841–860. (1989) Zbl0687.10004MR1024609
- Somer, L., On Lucas -pseudoprimes, In: Applications of Fibonacci numbers, vol. 7 (eds. G. E. Bergum, A. N. Philippou, A. F. Horadam), Kluwer Academic Publishers, Dordrecht 1998, 369–375. (1998) Zbl0919.11008MR1638463
- Steuerwald, R., Über die Kongruenz , S.-B. Math.-Nat. Kl., Bayer. Akad. Wiss. 1947, 177. (1947) Zbl0033.10501MR0030541
- Szymiczek, K., Note on Fermat numbers, Elem. Math. 21 (1966), 59. (1966) Zbl0142.28904MR0193056
- Szymiczek, K., 10.2307/2314051, Amer. Math. Monthly 74 (1967), 35–37. (1967) Zbl0146.26803MR0205921DOI10.2307/2314051
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