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ArticleOriginal scientific text

Title

Consecutive powers in continued fractions

Authors 1, 2

Affiliations

  1. Department of Mathematics & Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada
  2. Department of Computer Science, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada

Bibliography

  1. L. Bernstein, Fundamental units and cycles, J. Number Theory 8 (1976), 446-491.
  2. L. Bernstein, Fundamental units and cycles in the period of real quadratic number fields, Part II, Pacific J. Math. 63 (1976), 63-78.
  3. G. Chrystal, Textbook of Algebra, part 2, 2nd ed., Dover Reprints, N.Y., 1969, 423-490.
  4. M. D. Hendy, Applications of a continued fraction algorithm to some class number problems, Math. Comp. 28 (1974), 267-277.
  5. C. Levesque, Continued fraction expansions and fundamental units, J. Math. Phys. Sci. 22 (1988), 11-44.
  6. C. Levesque and G. Rhin, A few classes of periodic continued fractions, Utilitas Math. 30 (1986), 79-107.
  7. R. A. Mollin, Prime powers in continued fractions related to the class number one problem for real quadratic fields, C. R. Math. Rep. Acad. Sci. Canada 11 (1989), 209-213.
  8. R. A. Mollin, Powers in continued fractions and class numbers of real quadratic fields, Utilitas Math., to appear.
  9. R. A. Mollin and H. C. Williams, Powers of 2, continued fractions and the class number one problem for real quadratic fields ℚ(√d) with d ≡ 1 (mod 8), in: The Mathematical Heritage of C. F. Gauss, G. M. Rassias (ed.), World Sci., 1991, 505-516.
  10. O. Perron, Die Lehre von den Kettenbrüchen, Teubner, Stuttgart 1977.
  11. D. Shanks, The infrastructure of a real quadratic field and its applications, in: Proc. 1972 Number Theory Conf., Univ. of Colorado, Boulder, Colo., 1973, 217-224.
  12. H. C. Williams, A note on the period length of the continued fraction expansion of certain √D, Utilitas Math. 28 (1985), 201-209.
  13. H. C. Williams and M. C. Wunderlich, On the parallel generation of the residues for the continued fraction factoring algorithm, Math. Comp. 177(1987), 405-423.
Acta Arithmetica
1992/61/3
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Pages:
233-264
Main language of publication
English
Received
1990-09-07
Accepted
1991-10-24
Published
1992
Exact and natural sciences