14-term arithmetic progressions on quartic elliptic curves.
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MacLeod, Allan J. (2006)
Journal of Integer Sequences [electronic only]
R. J. Stroeker (1979)
Compositio Mathematica
J.B. Tunnell (1983)
Inventiones mathematicae
Bremner, Andrew (1986)
International Journal of Mathematics and Mathematical Sciences
Andrew Bremner, Patrick Morton (1983)
Manuscripta mathematica
J. MacLeod, Allan (2008)
Annales Mathematicae et Informaticae
Maciej Ulas (2009)
Colloquium Mathematicae
We show that the system of equations , where is a triangular number, has infinitely many solutions in integers. Moreover, we show that this system has a rational three-parameter solution. Using this result we show that the system has infinitely many rational two-parameter solutions.
Jianhua Chen (2001)
Acta Arithmetica
Huaming Wu, Maohua Le (1996)
Colloquium Mathematicae
Maohua Le (1995)
Colloquium Mathematicae
Andrej Dujella (2000)
Acta Arithmetica
Andrej Dujella, Borka Jadrijević (2002)
Acta Arithmetica
Gaál, István, Járási, István, Luca, Florian (2003)
Experimental Mathematics
MacLeod, Allan J. (2003)
Southwest Journal of Pure and Applied Mathematics [electronic only]
Savin, Diana (2009)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
S. Akhtari, A. Togbé, P. G. Walsh (2009)
Acta Arithmetica
D. Coray (1976)
Acta Arithmetica
J. Coates (1970)
Acta Arithmetica
Clemens Fuchs, Rafael von Känel, Gisbert Wüstholz (2011)
Acta Arithmetica
Yanfeng He, Wenpeng Zhang (2010)
Czechoslovak Mathematical Journal
The main purpose of this paper is to prove that the elliptic curve has only the integral points and , using elementary number theory methods and some known results on quadratic and quartic Diophantine equations.
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