On the Diophantine equation \(X^2-(p^{2m}+1)Y^6=-p^{2m}\)

DOI10.7169/facm/1285679144zbMath1213.11077OpenAlexW2052838796MaRDI QIDQ1959785

Pingzhi Yuan, Bo He, Alain S. Togbé

Publication date: 12 October 2010

Published in: Functiones et Approximatio. Commentarii Mathematici (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.facm/1285679144

zbMATH Keywords

hypergeometric functionsPadé approximationsThue equationhigher degree Diophantine equationhypergeometric method

Mathematics Subject Classification ID

Higher degree equations; Fermat's equation (11D41) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Cites Work

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• Complete solution of the diophantine equation \(X^ 2+1=dY^ 4\) and a related family of quartic Thue equations
• On the method of Thue-Siegel
• Rational and algebraic approximations of algebraic numbers and their application
• On algebraic approximations of certain algebraic numbers.
• On the Diophantine equation X²-(2^2m+1)Y⁴=-2^2m
• Thue's Fundamentaltheorem, I: The general case
• The Diophantine equation aX 4 – bY 2 = 1
• The method of Thue–Siegel for binary quartic forms
• Simple families of Thue inequalities
• Irrationality via the Hypergeometric method
• Some Remarks on the Diophantine Equations x ² − Dy ⁴ = 1 and x ⁴ − Dy ² = 1
• On the Diophantine Equation $Ax^4-By^2=C$, ($C=1,4$).

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