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Book Review

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Book Information:

Authors: Michael J. Jacobson, Jr. and Hugh C. Williams
Title: Solving the Pell equation
Additional book information: CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer, New York, 2009, xx+495 pp., ISBN 978-0-387-84922-5, US $59.95

References [Enhancements On Off] (What's this?)

  • [1] J.-L. de la Grange, Solution d'un problème d'arithmétique, Mélanges de philosophie et de mathématique de la Société Royale de Turin 4 (1766-1769), 44-97 (this paper was written and submitted for publication in 1768, and it appeared in 1773; see [12, Chapter IV, §II]); Œuvres, vol. I, Gauthier-Villars, Paris, 1867, 669-731.
  • [2] H.$ \,$E. Dudeney, Amusements in mathematics, Thomas Nelson and Sons, London, 1917.
  • [3] L. Euler, Vollständige Anleitung zur Algebra, St. Petersburg, 1770. A Russian translation had already appeared in 1768/69. Edition used: Opera omnia, series prima, volumen primum, H. Weber (ed.), B.$ \,$G. Teubner, Leipzig and Berlin, 1911.
  • [4] L. Euler, Elements of algebra, translated from the French [by J. Hewlett and F. Horner], two volumes, J. Johnson, London, 1797.
  • [5] J.$ \,$E. Hofmann, Studien zur Zahlentheorie Fermats (Über die Gleichung $ x^2=py^2+1$), Abh. Preuss. Akad. Wiss. Math.-Nat. Kl. 1944 (1944), no. 7, 19 pp.
  • [6] H.$ \,$W. Lenstra, On the calculation of regulators and class numbers of quadratic fields, J. Armitage (ed.), Journées Arithmétiques, 1980, London Math. Soc. Lecture Note Ser. 56, Cambridge University Press, Cambridge, 1982, 123-150.
  • [7] D. Mumford, The lure of the abstract: tracing the parallel influences of the Zeitgeist on art and mathematics in the last 200 years, unpublished lecture.
  • [8] J. Neukirch, Algebraische Zahlentheorie, Springer, Berlin, 1992. The English translation Algebraic number theory (1999) corrects the error, but the 2002 reprint of the German original doesn't; one senses the influence of the GCHQ.
  • [9] René Schoof, Computing Arakelov class groups, Algorithmic number theory: lattices, number fields, curves and cryptography, Math. Sci. Res. Inst. Publ., vol. 44, Cambridge Univ. Press, Cambridge, 2008, pp. 447–495. MR 2467554
  • [10] Daniel Shanks, The infrastructure of a real quadratic field and its applications, Proceedings of the Number Theory Conference (Univ. Colorado, Boulder, Colo., 1972) Univ. Colorado, Boulder, Colo., 1972, pp. 217–224. MR 0389842
  • [11] A. Weil, Number theory, an approach through history, Birkhäuser, Boston, 1984.

Review Information:

Reviewer: Hendrik Lenstra
Affiliation: Universiteit Leiden
Reviewer: Peter Stevenhagen
Affiliation: Universiteit Leiden
Journal: Bull. Amer. Math. Soc. 52 (2015), 345-351
Published electronically: December 19, 2014
Review copyright: © Copyright 2014 American Mathematical Society