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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Large integral points on elliptic curves

Author: Don Zagier
Journal: Math. Comp. 48 (1987), 425-436
MSC: Primary 11G05; Secondary 11D25, 11Y50
Addendum: Math. Comp. 51 (1988), 375.
MathSciNet review: 866125
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Abstract: We describe several methods which permit one to search for big integral points on certain elliptic curves, i.e., for integral solutions (x, y) of certain Diophantine equations of the form $ {y^2} = {x^3} + ax + b\;(a,b \in {\mathbf{Z}})$ in a large range $ \vert x\vert,\vert y\vert \leqslant B$, in time polynomial in $ \log \log B$. We also give a number of individual examples and of parametric families of examples of specific elliptic curves having a relatively large integral point.

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Article copyright: © Copyright 1987 American Mathematical Society