| Title:
|
On Lucas pseudoprimes of the form $ax^2+bxy+cy^2$ in arithmetic progression $AX+B$ with a prescribed value of the Jacobi symbol (English) |
| Author:
|
Rotkiewicz, A. |
| Language:
|
English |
| Journal:
|
Acta Mathematica et Informatica Universitatis Ostraviensis |
| ISSN:
|
1211-4774 |
| Volume:
|
10 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
103-109 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11A07 |
| MSC:
|
11A15 |
| MSC:
|
11B39 |
| idZBL:
|
Zbl 1028.11008 |
| idMR:
|
MR1943029 |
| . |
| Date available:
|
2009-01-30T09:09:47Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/120575 |
| . |
| Reference:
|
[1] BACHMANN P.: Zahlentheorie. 2, Die analytische Zahlentheorie.Tenbner, Leipzig, 1894. |
| Reference:
|
[2] Baillie R., Wagstaff, Jr. S.: Lucas pseudoprimes.Math. Comp. 35 (1980), 1391-1417. Zbl 0458.10003, MR 0583518, 10.1090/S0025-5718-1980-0583518-6 |
| Reference:
|
[3] Bilu Yu., Hanrot G., Vouter P. M.: Existence of primitive divisors of Lucas and Lehmer numbers.(with an appendix by Mignott M.), J. Reine Angew. Math. 539 (2001), 75-122. MR 1863855 |
| Reference:
|
[4] Crandall R., Pomerance C.: Prince Numbers.A Computational Perspective, Springer-Verlag, New York, 2001. MR 1821158 |
| Reference:
|
[5] Dickson L. E.: History of the Theory of Numbers, Vol. I.Chelsea Publishing Company, New York, 1952. |
| Reference:
|
[6] Durst L. K.: Exceptional real Lehmer sequences.Pacific J. Math. 9 (1959), 437-441. Zbl 0091.04204, MR 0108465, 10.2140/pjm.1959.9.437 |
| Reference:
|
[7] Erdös P., Kiss P., Sárközy A.: Lower bound for the counting function.Math. Comp. 51 (1988), 315-323. MR 0942158 |
| Reference:
|
[8] Lehmer D. H.: An extended theory of Lucas functions.Ann. of Math. (2) 31 (1930), 419-448. MR 1502953, 10.2307/1968235 |
| Reference:
|
[9] Meyer A.: Ueber einen Satz von Dinchlet.J. reine angew. Math. 103 (1888), 98-117. |
| Reference:
|
[10] Narkiewicz W.: The Development of Prime Number Theory: from Euclid to Hardy and Littlewood.Springer, 2000. Zbl 0942.11002, MR 1756780 |
| Reference:
|
[11] Rotkiewicz A.: On the pseudoprimes of the form ax + b with respect to the sequence of Lehmer.Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 20 (1972), 349-354. Zbl 0249.10012, MR 0309843 |
| Reference:
|
[12] Rotkiewicz A.: On Euler Lehmer pseudoprimes and strong Lehmer pseudoprimes with parameters L,Q in arithmetic progression.Math. Comp. 39 (1982), 239-247. MR 0658229 |
| Reference:
|
[13] Rotkoewicz A.: On strong pseudoprimes in the case of negative discriminant in arithmetic progressions.Acta Arith. 68 (1994), 145-151. MR 1305197 |
| Reference:
|
[14] Rotkiewicz A.: On Lucas pseudoprimes of the form $ax\sp 2+bxy+cy\sp 2$.Applications of Fibonacci Numbers, Volume 6, Edited by G.E. Bergum, A.N. Philippou and A.F. Horadam, Kluwer Academic Publishers, Dordrecht, 1996, 409-421. Zbl 0852.11006, MR 1393474 |
| Reference:
|
[15] Rotkiewicz A., A. Schinzel: Sur les nombres pseudopremiers de la forme $ax\sp 2+bxy+cy\sp 2$.C.R. Acad. Sci. Paris, 258 (1964), 3617-3620. MR 0161828 |
| Reference:
|
[16] Rotkiewicz A., Schinzel A.: On Lucas pseudoprimes with a prescribed value of the Jacobi symbol.Bull. Polish Acad. Sci. Math. 48 (2000), 77-80. Zbl 0951.11002, MR 1751157 |
| Reference:
|
[17] Schinzel A.: On primitive prime factors of $a^n - b^n$.Proc. Cambridge Philos. Soc. 58 (1962), 555-562. MR 0143728 |
| Reference:
|
[18] Schnitzel A.: The intrinsic divisors of Lehmer numbers in the case of negative discriminant.Ark. Math. 4 (1962), 413-416. MR 0139567, 10.1007/BF02591623 |
| Reference:
|
[19] Stewart C. L.: Primitive divisors of Lucas and Lehmer sequences.Transcendence Theory: Advances and Applications (A. Baker and D.W. Masser, eds.), Academic Press, New York, 1997, pp. 79-92. MR 0476628 |
| Reference:
|
[20] Ward M.: The intrinsic divisor of Lehmer numbers.Ann. of Math. (2) 62 (1955), 230-236. MR 0071446, 10.2307/1969677 |
| . |
