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Number-Theoretic Preliminaries

  • Song Y. Yan
Part of the Advances in Information Security book series (ADIS, volume 11)

Abstract

The theory of numbers is primarily the theory of the properties of integers (whole numbers), such as parity, divisibility, primality, additivity, multiplicativity, and unique factorization, etc. One of the important features of number theory is that problems in number theory are generally easy to state but often very difficult to solve.

Keywords

Elliptic Curve Elliptic Curf Residue Class Primitive Root Arithmetic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 13.
    A. Baker, AConcise Introduction to theTheory of Numbers, Cambridge University Press, 1984.Google Scholar
  2. 47.
    H. Davenport, The Higher Arithmetic, 7th Edition, Cambridge University Press, 1999.Google Scholar
  3. 153.
    J. H. Silverman, A Friendly Introduction toNumber Theory, Second Edition, Prentice-Hall, 2001.Google Scholar
  4. 78.
    K. Kato, N. Kurokawa and T. Saito, Number Theory 1: Fermat’s Dream, AMS, 2000.Google Scholar
  5. 68.
    G. H. Hardy and E. M. Wright, An Introduction to Theory of Numbers, 5th Edition, Oxford University Press, 1979.Google Scholar
  6. 40.
    H. Cohen, Advanced Number Theory, Dover Publications, 1980.Google Scholar
  7. 71.
    L. Hua, Introduction to Number Theory, English Translation from Chinese by P. Shiu, Springer-Verlag, 1980.Google Scholar
  8. 75.
    K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, 2nd Edition, Graduate Texts in Mathematics 84, Springer-Verlag, 1990.Google Scholar
  9. 112.
    I. Niven, H. S. Zuckerman and H. L. Montgomery, An Introduction to the Theory of Numbers, 5th Edition, John Wiley Sons, 1991.Google Scholar
  10. 139.
    H. E. Rose, A Course in Number Theory, 2nd Edition, Oxford University Press, 1994.Google Scholar
  11. 140.
    K. Rosen, Elementary Number Theory and its Applications, 4th Edition, Addison-Wesley, 2000.Google Scholar
  12. 165.
    J. Stillwell, Elements of Number Theory, Springer-Verlag, 2000.Google Scholar
  13. 74.
    D. Husemöller, Elliptic Curves, Graduate Texts in Mathematics 111, Springer-Verlag, 1987.Google Scholar
  14. 151.
    J. H. Silverman and J. Tate, Rational Points on Elliptic Curves, Undergraduate Texts in Mathematics, Springer-Verlag, 1992.zbMATHCrossRefGoogle Scholar
  15. 152.
    J. H. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics106, Springer-Verlag, 1994.Google Scholar
  16. 70.
    I. N. Herstein, Topics in Algebra, 2nd Edition, Wiley, 1975.Google Scholar
  17. 141.
    J. J. RotmanA First Course in Abstract Algebra, Second Edition, Prentice-Hall, 2000.Google Scholar
  18. 7.
    J. A. Anderson and J. M. Bell, Number Theory with Applications, Prentice-Hall, 1997.Google Scholar
  19. 8.
    G. E. Andrews, Number Theory. W. B. Sayders Company, 1971. Also Dover Publications, 1994.Google Scholar
  20. 9.
    T. M. Apostol, Introduction to Analytic Number Theory, Corrected 5th Printing, Undergraduate Texts in Mathematics, Springer-Verlag, 1998.zbMATHGoogle Scholar
  21. 39.
    L. Childs, AConcrete Introduction to Higher Algebra, 2nd Edition, Springer-Verlag, 2000.Google Scholar
  22. 49.
    L. E. Dickson, History of the Theory of Numbers I - Divisibility and Primality, G. E. Stechert & Co., New York, 1934.Google Scholar
  23. 52.
    P. G. L. Dirichlet, Lecturers on Number Theory. Supplements by R. Dedekind, American Mathematics Society and London Mathematics Society, 1999.Google Scholar
  24. 55.
    Euclid, The Thirteen Books of Euclid’s Elements, Translated by T. L. Heath, Great Books of the Western World 11, edited by R. M. Hutchins, William Benton Publishers, 1952.Google Scholar
  25. 60.
    C. F. Gauss, Disquisitiones Arithmeticae, G. Fleischer, Leipzig, 1801. English translation by A. A. Clarke, Yale University Press, 1966. Revised English translation by W. C. Waterhouse, Springer-Verlag, 1975.Google Scholar
  26. 67.
    G. H. Hardy, AMathematician’s Apology, Cambridge University Press, 1979.Google Scholar
  27. 76.
    T. H. Jackson, From Number Theory to Secret Codes, A Computer Illustrated Text, Adam Hilger, Bristol, 1987.zbMATHGoogle Scholar
  28. 82.
    N. Koblitz, Introduction toElliptic Curves and Modular Forms, 2nd Edition, Graduate Texts in Mathematics97, Springer-Verlag, 1993.Google Scholar
  29. 83.
    N. Koblitz, ACourse in Number Theory and Cryptography, 2nd Edition, Graduate Texts in Mathematics114, Springer-Verlag, 1994.Google Scholar
  30. 84.
    N. Koblitz, Algebraic Aspects of Cryptography, Algorithms and Computation in Mathematics3, Springer-Verlag, 1998.Google Scholar
  31. 103.
    R. A. Mollin, Fundamental Number Theory with Applications, CRC Press, 1998.Google Scholar
  32. 110.
    R. Motwani and P. Raghavan, Randomized Algorithms, Cambridge University Press, 1995.Google Scholar
  33. 111.
    M. B. Nathanson, Elementary Methods in Number Theory, Springer-Verlag, 2000.Google Scholar
  34. 116.
    O. Ore, Number Theory and its History, Dover Publications, 1988.Google Scholar
  35. 130.
    D. Redmond, Number Theory: An Introduction, Marcel Dekker, New York, 1996.zbMATHGoogle Scholar
  36. 131.
    P. Ribenboim, The Little Book on Big Primes, Springer-Verlag, 1991.Google Scholar
  37. 133.
    P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, 1996.Google Scholar
  38. 180.
    S. Y. Yan, Number Theory for Computing, 2nd Edition, Springer-Verlag, 2002.Google Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Song Y. Yan
    • 1
  1. 1.Coventry UniversityUK

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