PORTUGALIAE MATHEMATICA Vol. 58, No. 2, pp. 211218 (2001) 

Integer Points Unusually Close to Elliptic CurvesMarian Vâjâitu and Alexandru ZaharescuInstitute of Mathematics of the Romanian Academy,P.O. Box 1764, RO70700, Bucharest  ROMANIA Email: mvajaitu@stoilow.imar.ro Institute of Mathematics of the Romanian Academy, P.O. Box 1764, RO70700, Bucharest  ROMANIA and Institute for Advanced Study, School of Mathematics, Math. Building, Olden Lane, Princeton, New Jersey 08540  USA Email: 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
