On the Diophantine equation \(x^2 + 2^a \cdot 19^b = y^n\)

DOI10.1007/s13226-012-0013-4zbMath1291.11069OpenAlexW2046515981MaRDI QIDQ691675

Gökhan Soydan, Maciej Ulas, Huilin Zhu

Publication date: 3 December 2012

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13226-012-0013-4

zbMATH Keywords

class numberquadratic number fieldhigher degree Diophantine equationRamanujan-Nagell equation

Mathematics Subject Classification ID

Quadratic extensions (11R11) Class numbers, class groups, discriminants (11R29) Higher degree equations; Fermat's equation (11D41)

Related Items (7)

On the exponential Diophantine equation \(x^2 + 2^a p^b = y^n\) ⋮ Complete solution of the Diophantine Equation $x^{2}+5^{a}\cdot 11^{b}=y^{n}$ ⋮ On the diophantine equation $x^2+2^a3^b73^c=y^n $ ⋮ On the Diophantine equation \(X^{2N}+2^{2\alpha}5^{2\beta}p^{2\gamma}=Z^5\) ⋮ On the Diophantine equation \(x^2+3^a41^b=y^n\) ⋮ On Lebesgue–Ramanujan–Nagell Type Equations ⋮ On the solutions of certain Lebesgue-Ramanujan-Nagell equations

Uses Software

• Magma

Cites Work

• On the Diophantine equation \(x^2+5^a\cdot 11^b=y^n\)
• On some generalized Lebesgue-Nagell equations
• On the Diophantine equation \(x^2 + p^{2k} = y^n\)
• The diophantine equation \(x^ 2 + 2^ k = y^ n\)
• On Cohn's conjecture concerning the Diophantine equation \(x^2+2^m=y^n\)
• On the diophantine equation \(x^ 2+2^ k=y^ n\)
• The Magma algebra system. I: The user language
• On the equation \(x^2 + 2^a \cdot 3^b = y^n\)
• Existence of primitive divisors of Lucas and Lehmer numbers
• On the Diophantine equation x²+ 2^α13^β= yⁿ
• ON THE DIOPHANTINE EQUATION x² + 2^a · 5^b = yⁿ
• The diophantine equation x² + 19 = yⁿ
• On the Diophantine Equation x 2 + 2 α 5 β 13 γ  = y n
• ON THE DIOPHANTINE EQUATION x² + 5^a 13^b = yⁿ

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