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On the diophantine equation x 2 + 2 a · 19 b = y n

Author

Listed:
  • Gökhan Soydan

    (Işıklar Air Force High School)

  • Maciej Ulas

    (Jagiellonian University)

  • Hui Lin Zhu

    (Xiamen University)

Abstract

In this paper, we give all solutions of the Diophantine equation $$x^2 + 2^a \cdot 19^b = y^n , x \geqslant 1, y > 1, \gcd (x,y) = 1, n \geqslant 3, a,b \geqslant 0.$$

Suggested Citation

  • Gökhan Soydan & Maciej Ulas & Hui Lin Zhu, 2012. "On the diophantine equation x 2 + 2 a · 19 b = y n," Indian Journal of Pure and Applied Mathematics, Springer, vol. 43(3), pages 251-261, June.
    • Handle: RePEc:spr:indpam:v:43:y:2012:i:3:d:10.1007_s13226-012-0013-4
    DOI: 10.1007/s13226-012-0013-4
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    References listed on IDEAS

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    1. Florian Luca, 2002. "On the equation x 2 + 2 a â‹… 3 b = y n," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 29, pages 1-6, January.
    2. S. Akhtar Arif & Fadwa S. Abu Muriefah, 1997. "On the Diophantine equation x 2 + 2 k = y n," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 20, pages 1-6, January.
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