Arithmetic progressions formed by pseudoprimes
Acta Mathematica et Informatica Universitatis Ostraviensis (2000)
- Volume: 08, Issue: 1, page 61-74
- ISSN: 1804-1388
Access Full Article
topHow to cite
topRotkiewicz, Andrzej. "Arithmetic progressions formed by pseudoprimes." Acta Mathematica et Informatica Universitatis Ostraviensis 08.1 (2000): 61-74. <http://eudml.org/doc/23839>.
@article{Rotkiewicz2000,
author = {Rotkiewicz, Andrzej},
journal = {Acta Mathematica et Informatica Universitatis Ostraviensis},
keywords = {pseudoprime; super pseudoprime; prime pretender; Carmichael number; Fibonacci pseudoprime; Lucas pseudoprime; Lehmer pseudoprime; Fibonacci sequence; Lucas number; Lehmer number},
language = {eng},
number = {1},
pages = {61-74},
publisher = {University of Ostrava},
title = {Arithmetic progressions formed by pseudoprimes},
url = {http://eudml.org/doc/23839},
volume = {08},
year = {2000},
}
TY - JOUR
AU - Rotkiewicz, Andrzej
TI - Arithmetic progressions formed by pseudoprimes
JO - Acta Mathematica et Informatica Universitatis Ostraviensis
PY - 2000
PB - University of Ostrava
VL - 08
IS - 1
SP - 61
EP - 74
LA - eng
KW - pseudoprime; super pseudoprime; prime pretender; Carmichael number; Fibonacci pseudoprime; Lucas pseudoprime; Lehmer pseudoprime; Fibonacci sequence; Lucas number; Lehmer number
UR - http://eudml.org/doc/23839
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., Jr., 10.1090/S0025-5718-1980-0583518-6, Math. Comp. 35 (1980), 1391-1417. (1980) Zbl0458.10003MR0583518DOI10.1090/S0025-5718-1980-0583518-6
- BEEGER N.G.W.R., 10.2307/2306320, Amer. Math. Monthly 58 (1951), 553-555. (1951) MR0043798DOI10.2307/2306320
- Carmichael R.D., 10.2307/1967797, Ann. of Math. (2) 15 (1913), 30-70. (1913) MR1502458DOI10.2307/1967797
- Chowla S., There exists an infinity of 3-combinations of primes in A.P., Proc Lahore Philos. Ser. 6, no 2 (1944), 15-16. (1944) Zbl0063.00875MR0014125
- ClPOLLA M., Sui numeri composti P che verificiano la congruenza di Fermat , Annali di Matematica (3) 9 (1904), 139-160. (1904)
- Conway J.H., Guy R.K., Schneeberger W.A., Sloane N.J.A., The primary pretenders, Acta Arith. 78 (1997), 307-313. (1997) Zbl0863.11005MR1438588
- Dickson L.E., A new extension of Dirichlet's theorem on prime numbers, Messenger Math. 33 (1904), 155-161. (1904)
- Dickson L.E., History of the Theory of Numbers, 3 vols., Washington 1919- 1923, reprint New York 1966. (1919)
- Duparc H.J.A., On almost primes of the second order, Math. Centrum Amsterdam. Rap. ZW 1955-013, (1955), 1-13 . (1955) Zbl0067.27303
- Duparc H.J.A., A remark to report Z.W.-013, Math. Centrum Amsterdam, Rap. Z.W. 1956-008. (1956)
- Durst L.K., 10.2140/pjm.1959.9.437, Pacific J. Math. 9 (1959), 437-441. (1959) Zbl0091.04204MR0108465DOI10.2140/pjm.1959.9.437
- Erdos P., 10.2307/2307640, Amer. Math. Monthly 57 (1950), 404-407. (1950) MR0036259DOI10.2307/2307640
- GRANVILLE A.J., The prime k-tuplets conjecture implies that there are arbitrarily long arithmetic progressions of Carmichael numbers, (written communication of December 1995). (1995)
- Heath-Brown D.R., 10.1112/jlms/s2-23.3.396, J. London Math. Soc, (2) 23 (1981), 396-414. (1981) Zbl0425.10051MR0616545DOI10.1112/jlms/s2-23.3.396
- Jeans J.A., The converse of Fermat's theorem, Messenger of Mathematics 27 (1898), p. 174.
- Kernbaum S., O szeregu Fibonacciego i jego uogolnieniach, Wiadom. Mat. 24 (1920), 203-217, II ibid. 25 (1921), 49-68. (1920)
- Korselt A., Probleme chinois, L'intermediare des mathematiciens 6 (1899), 142-143.
- Lehmer D.H., 10.2307/1968235, Ann. of Math. 31 (1930), 419-448. (1930) MR1502953DOI10.2307/1968235
- Lehmer E., On the infinitude of Fibonacci pseudoprimes, Fibonacci Quart. 2 (1964), 229-230. (1964)
- Lehmer D.H., 10.1017/S1446788700019364, J. Austral. Math. Soc Ser. A 21 (1978), 508-510. (1978) MR0417032DOI10.1017/S1446788700019364
- McDaniel W.L., 10.1090/S0025-5718-1989-0968152-6, Math. Comp. 53 (1989), 407-409. (1989) Zbl0678.10003MR0968152DOI10.1090/S0025-5718-1989-0968152-6
- Mahnke D., Leibniz and der Suché nach einer allgemeinem Primzahlgleichung, Bibliotheca Math. Vol. 13 (1913), 29-61. (1913)
- Needham J., Science and Civilization in China, vol. 3: Mathematics and Sciences of the Heavens and the Earth, Cambridge 1959, p. 54, footnote A. (1959) MR0139507
- Niewiadomski R., Spostrzezenia nad liczbami szeregu Fibonacciego, Wiadom. Mat. 15 (1911), 225-233. (1911)
- RlBENBOIM P., The New Book of Prime Number Records, Springer-Verlag, New York - Heidelberg - Berlin, 1996. (1996) MR1377060
- Rotkiewicz A., Sur les formules donnant des nombres pseudopremiers, Colloq. Math. 12 (1964), 69-72. (1964) Zbl0129.02703MR0166138
- ROTKIEWICZ A., Sur les progressions arithmétiques et géométriques formées de trois nombres pseudopremiers distincts, Acta Arith. 10 (1964), 325-328. (1964) Zbl0125.02304MR0171768
- Rotkiewicz A., On arithmetical progressions formed by k different pseudo-primes, J. Math. Sci. 4 (1969), 5-10. (1969) MR0250987
- Rotkiewicz A., Pseudoprime numbers and their generalizations, Student Association of the Faculty of Sciences, University of Novi Sad, Novi Sad 1972, pp. i+169. (1972) Zbl0324.10007MR0330034
- Rotkiewicz A., On the pseudoprimes of the form with respect to the sequence of Lehmer, Bull. Acad. Polon. Sci. Sér. Math. Astronom. Phys. 20 (1972), 349-354. (1972) Zbl0249.10012MR0309843
- Rotkiewicz A., 10.1007/BF02849586, Rend. Circ Mat. Palermo (2) 28 (1979), 62-64. (1979) MR0564551DOI10.1007/BF02849586
- Rotkiewicz A., 10.1007/BF02849758, Rend. Circ. Mat. Palermo (2) 29 (1980), 420-426. (1980) MR0638680DOI10.1007/BF02849758
- Rotkiewicz A., On Euler Lehmer pseudoprimes and strong Lehmer pseudoprimes with parameters in arithmetic progression, Math. Comp. 39 (1982), 239-247. (1982) MR0658229
- Rotkiewicz A., On strong Lehmer pseudoprimes in the case of negative discriminant in arithmetic progressions, Acta Arith. 68 (1994), 145-151. (1994) Zbl0822.11016MR1305197
- Rotkiewicz A., Arithmetical progressions formed by k different pseudoprimes, Rend. Circ. Mat. Palermo (2) 43 (1994), 391-402. (1994) MR1344876
- Rotkiewicz A., Ziemak K., On even pseudoprimes, The Fibonacci Quarterly, 33 (1995), 123-125. (1995) Zbl0827.11003MR1329016
- Rotkiewicz A., 10.1007/978-94-011-5020-0_37, Applications of Fibonacci Numbers, Volume 7, Edited by G.E. Bergum, A.N. Philippou and A.F. Horadam, Kluwer Academic Publishers, Dordrecht, the Netherlands 1998, 327-332. (1998) Zbl0926.11004MR1638459DOI10.1007/978-94-011-5020-0_37
- ROTKIEWICZ A., Arithmetical progression formed by Lucas pseudoprimes, Number Theory, Diophantine, Computational and Algebraic Aspects, Editors: Kálmán Gyóry, Attila Pethó and Vera T. Sos, Walter de Gruyter GmbH & Co., Berlin, New York 1998, 465-472. (1998) MR1628862
- Rotkiewicz A., Periodic sequences of pseudoprimes connected with Carmichael numbers and the least period of the function , Acta Arith. 91 (1999), 75-83. (1999) MR1726476
- Rotkiewicz A., Schinzel A., Lucas pseudoprimes with a prescribed value of the Jacobi symbol, Bull. Polish Acad. Sci. Math. 48 (2000), 77-80. Zbl0951.11002MR1751157
- Schinzel A., 10.1007/BF02591623, Ark. Mat. 4 (1962), 413-416. (1962) Zbl0106.03105MR0139567DOI10.1007/BF02591623
- Schinzel A., On primitive prime factors of Lehmer numbers I, Acta Arith. 8 (1963), 213-223. (1963) Zbl0118.27901MR0151423
- Schinzel A., Sierpiňski W., Sur certaines hypotheses concernant les nombres premiers, Acta Arith. 4 (1958), 185-208, and corrigendum, ibidem 5 (1960), 259. (1958) MR0106202
- SlERPlNSKl W., Remarque sur une hypothěse des Chinois concernant les nombres , Colloq. Math. 1 (1947), 9. (1947)
- SlERPlNSKl W., Elementary Theory of Numbers, Monografie Matematyczne 42, PWN, Warsaw 1964 (second edition: North-Holland, Amsterdam, New York, Oxford 1987). (1964) MR0930670
- Steuerwald R., Über die Kongruenz , Sitz.-Ber. math. naturw. Kl. Bayer. Akad. Wiss. Munchen 1947, 177. (1947) MR0030541
- Szymiczek K., Kilka twierdzen o liczbach pseudopierwszych, Zeszyty naukowe Wyzszej Szkoly Pedagogicznej w Katowicach, Sekcja Matematyki, Zeszyt Nr 5 (1966), 39-46. (1966)
- Szymiczek K., Note on Fermat numbers, Elem. Math. 21 (1966), 59. (1966) Zbl0142.28904MR0193056
- Van der Corput J.G., 10.1007/BF01597346, Math. Ann. 116 (1939), 1-50. (1939) MR1513216DOI10.1007/BF01597346
- Ward M., 10.2307/1969677, Ann. of Math. (2) 62 (1955), 230-236. (1955) MR0071446DOI10.2307/1969677
- ZSIGMONDY K., 10.1007/BF01692444, Monatsh. Math. 3 (1892), 265-284. MR1546236DOI10.1007/BF01692444
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.