PORTUGALIAEMATHEMATICA
Vol. 58, No. 2, pp. 211-218 (2001)
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PORTUGALIAE MATHEMATICA Vol. 58, No. 2, pp. 211-218 (2001) |
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Integer Points Unusually Close to Elliptic CurvesMarian Vâjâitu and Alexandru ZaharescuInstitute of Mathematics of the Romanian Academy,P.O. Box 1-764, RO-70700, Bucharest -- ROMANIA E-mail: mvajaitu@stoilow.imar.ro Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700, Bucharest -- ROMANIA and Institute for Advanced Study, School of Mathematics, Math. Building, Olden Lane, Princeton, New Jersey 08540 -- USA E-mail: zaharesc@ias.edu Abstract: We consider an elliptic curve $E_{\alpha,\beta}$ given by the equation $Y^2=X^3+\alpha X+\beta$, where $\alpha,\beta$ are real numbers, and look for integer points close to the curve. In case the diophantine type of $\alpha$ is larger than 4 we find infinitely many integer points unusually close to $E_{\alpha,\beta}$ or to the curve $E_{-\alpha,\beta}$. Full text of the article:
Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.
© 2001 Sociedade Portuguesa de Matemática
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