The size of the fundamental solutions of consecutive Pell equations

Experimental Mathematics

Volumn 9, Issue 4, 2000, Pages 631-640

  Jacobson, Michael J ^a   Williams, Hugh C ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

Author keywords

Continued fractions; Pell equation; Real quadratic field

Indexed keywords

EID: 0034348625     PISSN: 10586458     EISSN: None     Source Type: Journal    
DOI: 10.1080/10586458.2000.10504666     Document Type: Article

References (21)

1. [Bach 1990] E. Bach, "Explicit bounds for primality testing and related problems", Math. Comp. 55:191 (1990), 355-380.
2. [Beiler 1964] A. H. Beiler, Recreations in theory of numbers: the queen of mathematics entertains, Dover, New York, 1964.
3. [Carmichael 1959] R. D. Carmichael, The theory of numbers and Diophantine analysis, Dover Publications Inc., New York, 1959.
4. [Cohen and Lenstra 1984] H. Cohen and H. W. Lenstra, Jr., "Heuristics on class groups of number fields", pp. 33-62 in Number theory (Noordwijkerhout, 1983), edited by H. Jager, Lecture notes in Math. 1068, Springer, Berlin, 1984.
5. [Cohn 1962] H. Cohn, A second course in number theory, Wiley, New York, 1962.
6. [Fung and Williams 1990] G. W. Fung and H. C. Williams, "Quadratic polynomials which have a high density of prime values", Math. Comp. 55:191 (1990), 345-353.
7. [Halter-Koch 1989] F. Halter-Koch, "Reell-quadratische Zahlkörper mit großer Grundeinheit", Abh. Math. Sem. Univ. Hamburg 59 (1989), 171-181.
8. [Jacobson 1999] M. J. Jacobson, Jr., Subexponential class group computation in quadratic orders, Shaker Verlag, Aachen, 1999. Ph.D. Thesis, Technische Universität Darmstadt, Germany.
9. [Jacobson et al. 1995] M. J. Jacobson, Jr., R. F. Lukes, and H. C. Williams, "An investigation of bounds for the regulator of quadratic fields", Experiment. Math. 4:3 (1995), 211-225.
10. χ with prime modulus", J. Number Theory 2 (1970), 58-73.
11. [Lehmer 1928] D. H. Lehmer, "On the multiple solutions of the Pell equation", Annals of Math. 30 (1928), 66-72.
12. [LiDIA 1997] The LiDIA Group, "LiDIA: a C++ library for computational number theory", software, Technische Universität Darmstadt, Germany, 1997. See http://www.informatik.tu-darmstadt.de/TI/LiDIA.
13. [Littlewood 1928] J. E. Littlewood, "On the class number of the corpus P(√-k)", Proc. London Math. Soc. 27 (1928), 358-372.
14. [Lukes et al. 1995] R. F. Lukes, C. D. Patterson, and H. C. Williams, "Numerical sieving devices: their history and some applications", Nieuw Arch. Wish. (4) 13:1 (1995), 113-139.
15. [Lukes et al. 1996] R. F. Lukes, C. D. Patterson, and H. C. Williams, "Some results on pseudosquares", Math. Comp. 65:213 (1996), 361-372, S25-S27.
16. [Mollin 1996] R. A. Mollin, Quadratics, CRC Press, Boca Raton, FL, 1996.
17. [Roberts 1992] J. Roberts, Lure of the integers, Mathematical Association of America, Washington, DC, 1992.
18. 2 + a", Math. Comp. 14 (1960), 320-332.
19. χ)", pp. 267-283 in Analytic number theory (St. Louis, MO, 1972), edited by H. G. Diamond, Proc. Sympos. Pure Math. 24, Amer. Math. Soc., Providence, 1973.
20. [Stephens and Williams 1988] A. J. Stephens and H. C. Williams, "Some computational results on a problem concerning powerful numbers", Math. Comp. 50:182 (1988), 619-632.
21. [Yamamoto 1971] Y. Yamamoto, "Real quadratic number fields with large fundamental units", Osaka J. Math. 8 (1971), 261-270.