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
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/BFb0073793
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57359-3
Online ISBN: 978-3-540-48083-9
eBook Packages: Springer Book Archive