On the sum of consecutive cubes being a perfect square
R. J. Stroeker (1995)
Compositio Mathematica
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Displaying similar documents to “Solving elliptic diophantine equations: the general cubic case”
On the sum of consecutive cubes being a perfect square
On elliptic diophantine equations that defy Thue's method: The case of the Ochoa curve.
Stroeker, Roel J., de Weger, Benjamin M.M. (1994)
Experimental Mathematics
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Integral points on elliptic curves defined by simplest cubic fields.
Duquesne, Sylvain (2001)
Experimental Mathematics
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Solving elliptic diophantine equations avoiding Thue equations and elliptic logarithms.
de Weger, Benjamin M.M. (1998)
Experimental Mathematics
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On a characterization of Shimura's elliptic curve over ℚ(√37)
Masanari Kida (1996)
Acta Arithmetica
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On the elliptic logarithm method for elliptic Diophantine equations: reflections and an improvement.
Stroeker, Roel J., Tzanakis, Nikos (1999)
Experimental Mathematics
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-integral points on elliptic curves - Notes on a paper of B. M. M. de Weger
Emanuel Herrmann, Attila Pethö (2001)
Journal de théorie des nombres de Bordeaux
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In this paper we give a much shorter proof for a result of B.M.M de Weger. For this purpose we use the theory of linear forms in complex and -adic elliptic logarithms. To obtain an upper bound for these linear forms we compare the results of Hajdu and Herendi and Rémond and Urfels.
The D(1)-extensions of D(-1)-triples 1,2,c and integer points on the attached elliptic curves
Yasutsugu Fujita (2007)
Acta Arithmetica
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On the equation aX⁴-bY² = 2
S. Akhtari, A. Togbé, P. G. Walsh (2008)
Acta Arithmetica
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Good reduction of elliptic curves over imaginary quadratic fields
Masanari Kida (2001)
Journal de théorie des nombres de Bordeaux
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We prove that the -invariant of an elliptic curve defined over an imaginary quadratic number field having good reduction everywhere satisfies certain Diophantine equations under some hypothesis on the arithmetic of the quadratic field. By solving the Diophantine equations explicitly in the rings of quadratic integers, we show the non-existence of such elliptic curve for certain imaginary quadratic fields. This extends the results due to Setzer and Stroeker.
of elliptic curves with sufficient torsion over
Raymond Ross (1992)
Compositio Mathematica
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