Abstract
The equations considered in this chapter are in essence different both from the Thue equation and from its direct generalisations. It is possible to prove the existence of an effective bound for solutions of these equations by purely arithmetic methods, by reducing them to the Thue equation or to its generalisations over relative fields. However the bounds obtained in this way are not quite satisfactory in the general case, and we again turn to exponential equations to obtain better results. We give an analysis of the hyperelliptic equation and of integer and S-integer points on elliptic curves.
Keywords
- Prime Ideal
- Simple Root
- Elliptic Curf
- Algebraic Number
- Diophantine Equation
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© 1993 Springer-Verlag
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Sprindžuk, V.G. (1993). Elliptic and hyperelliptic equations. In: Talent, R. (eds) Classical Diophantine Equations. Lecture Notes in Mathematics, vol 1559. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073792
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DOI: https://doi.org/10.1007/BFb0073792
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57359-3
Online ISBN: 978-3-540-48083-9
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