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Diophantine equation X4+Y4 = 2(U4 + V4)

  • Farzali Izadi EMAIL logo and Kamran Nabardi
Published/Copyright: August 17, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 3

Abstract

In this paper, the theory of elliptic curves is used for finding the solutions of the quartic Diophantine equation X4+Y4 = 2(U4 + V4).

MSC 2010: Primary 11D45; Secondary 11G05
Key words: Diophantine equation; elliptic curve; congruent number

(Communicated by Stanislav Jakubec)

References

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Received: 2012-11-23
Accepted: 2013-11-7
Published Online: 2016-8-17
Published in Print: 2016-6-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0157
Keywords for this article
Diophantine equation; elliptic curve; congruent number

Articles in the same Issue

  1. Research Article
  2. On the vertex-to-edge duality between the Cayley graph and the coset geometry of von Dyck groups
  3. Research Article
  4. Characterization of hereditarily reversible posets
  5. Research Article
  6. Families of sets which can be represented as sublattices of the lattice of convex subsets of a linearly ordered set
  7. Research Article
  8. Diophantine equation X4+Y4 = 2(U4 + V4)
  9. Research Article
  10. On the congruent number problem over integers of cyclic number fields
  11. Research Article
  12. On the Diophantine equation x2 + C= yn for C = 2a3b17c and C = 2a13b17c
  13. Research Article
  14. Representations and evaluations of the error term in a certain divisor problem
  15. Research Article
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  17. Research Article
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  19. Research Article
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  31. Research Article
  32. Oscillation criteria for higher-order nonlinear delay dynamic equations on time scales
  33. Research Article
  34. Multiplier spaces and the summing operator for series
  35. Research Article
  36. Weighted αβ-statistical convergence of Kantorovich-Mittag-Leffler operators
  37. Research Article
  38. The local spectral radius of a nonnegative orbit of compact linear operators
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