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Equations of hyperelliptic type

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Part of the Lecture Notes in Mathematics book series (3157,volume 1559)

Abstract

We apply the methods and considerations described in the previous chapter to more general situations so as to obtain new facts generalising our former results. Then we proceed to a new type of equations in which at least one of the unknowns is a power of an unknown integer. Our aim is to bound the unknown exponent so as to reduce these new equations to those of the kind considered before. In this way we determine, for example, that any integral polynomial having at least two simple roots represents only a finite number of powers of integers with exponents greater than 2. We also give an analysis of S-integer solutions of the Catalan equation. *** DIRECT SUPPORT *** A00I6B17 00003

Keywords

  • Prime Number
  • Prime Ideal
  • Simple Root
  • Prime Divisor
  • Principal Ideal

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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© 1993 Springer-Verlag

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Sprindžuk, V.G. (1993). Equations of hyperelliptic type. In: Talent, R. (eds) Classical Diophantine Equations. Lecture Notes in Mathematics, vol 1559. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073793

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  • DOI: https://doi.org/10.1007/BFb0073793

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57359-3

  • Online ISBN: 978-3-540-48083-9

  • eBook Packages: Springer Book Archive