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

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Abstract

In this paper, we give all solutions of the Diophantine equation

$$x^2 + 2^a \cdot 19^b = y^n , x \geqslant 1, y > 1, \gcd (x,y) = 1, n \geqslant 3, a,b \geqslant 0.$$

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Authors and Affiliations

  1. Işıklar Air Force High School, 16039, Bursa, Turkey

    Gökhan Soydan

  2. Faculty of Mathematics and Computer Science, Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348, Kraków, Poland

    Maciej Ulas

  3. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, P.R. China

    Hui Lin Zhu

Authors
  1. Gökhan Soydan
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  2. Maciej Ulas
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  3. Hui Lin Zhu
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Correspondence to Gökhan Soydan.

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Soydan, G., Ulas, M. & Zhu, H.L. On the diophantine equation x 2 + 2a · 19b = y n . Indian J Pure Appl Math 43, 251–261 (2012). https://doi.org/10.1007/s13226-012-0013-4

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  • DOI: https://doi.org/10.1007/s13226-012-0013-4

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