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

Gökhan Soydan (), Maciej Ulas () and Hui Lin Zhu ()
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Gökhan Soydan: Işıklar Air Force High School
Maciej Ulas: Jagiellonian University
Hui Lin Zhu: Xiamen University

Indian Journal of Pure and Applied Mathematics, 2012, vol. 43, issue 3, 251-261

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

Keywords: Diophantine equation; quadratic number field; class number; Ramanujan-Nagell equation (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s13226-012-0013-4

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