• Serge Lang
Part of the Undergraduate Texts in Mathematics book series (UTM)


Let K be a field. Every reader of this book will have written expressions like
$${a_n}{t^n} + {a^{n - 1}} + ... + {a_{0,}}$$
where a 0,...,a n are real or complex numbers. We could also take these to be elements of K. But what does “t” mean? Or powers of “t” like t, t 2,...,t n ?


Finite Field Polynomial Ring Unique Factorization Prime Element Great Common Divisor 
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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  1. [Bchs]
    B. Birch, S. Chowla, M. Hall, A. Schinzel, On the difference x3 y 2, Norske Vid. Selsk. Forrh. 38 (1965) pp. 65 - 69MathSciNetMATHGoogle Scholar
  2. [Blstw]
    Brillhart, D. H. Lehmer, J. L. Selfridge, B. Tuckerman, and S. S. Wagstaff Jr., Factorization of b ± 1, b = 2, 3, 5, 6, 7, 10, 11 up to high powers,Contemporary Mathematics Vol. 22, Ams, Providence, RI 1983Google Scholar
  3. [Dan]
    L. V. Danilov, The diophantine equation x 3 — y 2 = k and Halls conjecture, Mat. Zametki Vol. 32 No. 3 (1982) pp. 273 - 275MathSciNetMATHGoogle Scholar
  4. [Day]
    H. Davenport, On f 3 (t) — g 2 (t), K. Norske Vod. Selskabs Farh. (Trondheim), 38 (1965) pp. 86 - 87MathSciNetMATHGoogle Scholar
  5. [Fr]
    G. Frey, Links between stable elliptic curves and elliptic curves, Number Theory, Lecture Notes Vol. 1380, Springer-Verlag, Ulm 1987 pp. 31 - 62Google Scholar
  6. [Ha]
    M. Hall, The diophantine equation x 3 — y 2 = k, Computers in Number Theory, ed. by A. O. L. Atkin and B. Birch, Academic Press, London 1971 pp. 173 - 198MATHGoogle Scholar
  7. [La]
    S. Lang, Old and new conjectured diophantine inequalities, Bull. Amer. Math. Soc. (1990)Google Scholar
  8. [StT 86]
    C. L. Stewart and R. Tijdeman, On the Oesterle-Masser Conjecture, Monatshefte fur Math. (1986) pp. 251 - 257Google Scholar
  9. [Ti 89]
    R. Tijdeman, Diophantine Equations and Diophantine Approximations, [Banff]lecture in Number Theory and its Applications, ed. R. A. Mollin, Kluwer Academic Press, 1989 see especially p. 234Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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