Method of infinite ascent applied on A3 ± nB2 = C3

Susil Kumar Jena
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 19, 2013, Number 2, Pages 10—14
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Authors and affiliations

Susil Kumar Jena
Department of Electronics and Telecommunication Engineering
KIIT University, Bhubaneswar 751024, Odisha, India

Abstract

In this paper we will produce different formulae for which the Diophantine equation A3 ± nB2 = C3 will generate infinite number of co-prime integral solutions for (A, B, C) for any positive integer n.

Keywords

  • Method of infinite ascent
  • Diophantine equations A3 ± nB2 = C3

AMS Classification

  • 11D41

References

  1. Beukers, F. The Diophantine equation Axp + Byq = Czr, Duke Math. J., Vol. 91, 1998, 61–88.
  2. Bruin, N. On powers as sums of two cubes, ANTS IV, Leiden, 2000, Lecture Notes in Comp. Sci., Springer, Vol. 1838, 2000, 169–184.
  3. Bruin, N. Chabauty methods using elliptic curves, J. reine angew. Math., Vol. 562, 2003, 27–49.
  4. Jena, S. K. Method of Infinite Ascent applied on mA6 + nB3 = C2, The Math. Stud., Vol. 77, 2008, No. 1–4, 239–246.
  5. Jena, S. K. Method of Infinite Ascent applied on A4 ± nB2 = C3, The Math. Stud., Vol. 78, 2009, No. 1–4, 233–238.
  6. Jena, S. K. Method of Infinite Ascent applied on mA3 + nB3 = C2, The Math. Stud., Vol. 79, 2010, No. 1–4, 187–192.
  7. Jena, S. K. Method of Infinite Ascent applied on mA3 + nB3 = 3C2, The Math. Stud., Vol. 81, 2012, No. 1–4 (To appear).
  8. Kraus, A. Sur l’equation a3 + b3 = cp, Experiment Math. J., Vol. 71, 1998, No. 1, 1–13. 14

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Cite this paper

APA

Jena, S. K. (2013). Method of infinite ascent applied on A3 ± nB2 = C3. Notes on Number Theory and Discrete Mathematics, 19(2), 10-14.

Chicago

Jena, Susil Kumar. “Method of Infinite Ascent Applied on A3 ± nB2 = C3.” Notes on Number Theory and Discrete Mathematics 19, no. 2 (2013): 10-14.

MLA

Jena, Susil Kumar. “Method of Infinite Ascent Applied on A3 ± nB2 = C3.” Notes on Number Theory and Discrete Mathematics 19.2 (2013): 10-14. Print.

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