On the Diophantine equation \(x^ 2+a^ 2=2y^ p\).

DOI10.1016/S0019-3577(04)90021-3zbMath1088.11021OpenAlexW2074325239MaRDI QIDQ1890430

Szabolcs Tengely

Publication date: 3 January 2005

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0019-3577(04)90021-3

zbMATH Keywords

exponential Diophantine equationsDiophantine approximations

Mathematics Subject Classification ID

Cubic and quartic Diophantine equations (11D25) Higher degree equations; Fermat's equation (11D41)

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Cites Work

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• On the Diophantine equation \(x^2+q^{2k+1}=y^n\)
• Solving Thue equations of high degree
• The diophantine equation \(x^ 2 + 2^ k = y^ n\)
• The diophantine equation \(x^2+5^{2k+1}= y^n\)
• On the diophantine equation \(x^ 2+2^ k=y^ n\)
• The diophantine equation \(x^2+3^m=y^n\)
• On the Diophantine equation \(x^2+2=y^n\)
• The Diophantine equation \(x^2+2^k=y^n\). II
• On the equation \(x^2 + 2^a \cdot 3^b = y^n\)
• Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation
• On the Diophantine equation \(x^2+2^k=y^n\). II
• The Diophantine equation \(Ax^ p+By^ q=Cz^ r\).
• On the Diophantine equation \(Cx^ 2 +D = y^ n\)
• Verallgemeinerung eines Fermatschen Satzes
• Existence of primitive divisors of Lucas and Lehmer numbers
• On the equation $y^m = P(x)$
• A corollary to a theorem of Laurent-Mignotte-Nesterenko
• Thue equations with composite fields
• The diophantine equation x² + C = yⁿ
• On the diophantine equation $x^2 - p^m = ±y^n$
• On a diophantine equation
• On the Diophantine equation x²+7=y^m
• The diophantine equation x²+C=yⁿ, II
• On an diophantine equation
• Solving Thue equations without the full unit group
• On the Equations z^m = F (x, y ) and Ax^p + By^q = Cz^r
• Perfect Pell Powers
• On the Diophantine Equation $Cx^2 + D = 2y^n$.
• On the Diophantine equation \(Ax^2+2^{2m}=y^n\)

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