Solving elliptic diophantine equations: the general cubic case
نویسندگان
چکیده
منابع مشابه
Solving Elliptic Diophantine Equations Avoiding Thue Equations and Elliptic Logarithms
This research was supported by the Netherlands Mathematical Research Foundation SWON with nancial aid from the Netherlands Organization for Scienti c Research NWO. We determine the solutions in integers of the equation y = (x + p)(x + p) for p = 167, 223, 337, 1201. The method used was suggested to us by Yu. Bilu, and is shown to be in some cases more efficient than other general purpose method...
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1. Introduction. In [Z], Zagier describes several methods for explicitly computing (large) integral points on models of elliptic curves defined over Q. Here we are interested in the computation of all integral points on a given Weierstraß equation for an elliptic curve E/Q, but not merely by reducing the original diophantine equation to an equivalent finite set of Thue equations which are subse...
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In order to compute all integer points on a Weierstraß equation for an elliptic curve E/Q, one may translate the linear relation between rational points on E into a linear form of elliptic logarithms. An upper bound for this linear form can be obtained by employing the Néron-Tate height function and a lower bound is provided by a recent theorem of S. David. Combining these two bounds allows for...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1999
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-87-4-339-365