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Experimental Mathematics Volume 15, 2006 - Issue 4
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Original Article

On Simultaneous Arithmetic Progressions on Elliptic Curves

Irene García-Selfa Departamento de Álgebra, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160. 41080 Sevilla, Spain
&
José M. Tornero Departamento de Álgebra, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160. 41080 Sevilla, Spain
Pages 471-478 | Published online: 30 Jan 2011

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  • A. Bremner. "On Arithmetic Progressions on Elliptic Curves." Experiment. Math. 8:4 (1999), 409–413.
  • A. Bremner. "On Squares of Squares II." Acta Arith. 99:3 (2001), 289–308.
  • A. Bremner, J. H. Silverman, and N. Tzanakis. "Integral Points in Arithmetic Progression on y 2 = x(x 2 - n 2)." J. Number Theory 80 (2000), 187–208.
  • G. Campbell. "A Note on Arithmetic Progressions on Elliptic Curves." J. Integer Seq. 6 (2003), 03.1.3.
  • I. García–Selfa and J. M. Tornero. "Searching for Simultaneous Arithmetic Progressions on Elliptic Curves." Bull. Austral. Math. Soc. 71 (2005), 417–424.
  • I. García–Selfa and J. M. Tornero. Supplement to this article. Available online (www.expmath.org/expmath/volumes/15/15.4/tornero/list6ap.pdf).
  • I. García–Selfa, and J. M. Tornero. Supplement to this article. Available online (www.expmath.org/expmath/volumes/15/15.4/tornero/list6ap.txt).
  • J. B. Lee and W. Y. Vélez. "Integral Solutions in Arithmetic Progression for y 2 = x 3 +k." Period. Math. Hungar. 25 (1992), 31–49.
  • S. P. Mohanty. "On Consecutive Integral Solutions for y 2 = x 3 + k." Proc. Amer. Math. Soc. 48 (1975), 281–285.
  • J. H. Silverman. The Arithmetic of Elliptic Curves. New York: Springer, 1986.
  • M. P. Young. "Low-Lying Zeros of Families of Elliptic Curves." J. Amer. Math. Soc. 19 (2006), 205–250.

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