The regularity of Diophantine quadruples

DOI10.1090/tran/7069zbMath1417.11024OpenAlexW2523300211MaRDI QIDQ4608758

Yasutsugu Fujita, Takafumi Miyazaki

Publication date: 28 March 2018

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/tran/7069

zbMATH Keywords

linear forms in logarithmsDiophantine tuplessystem of Pellian equationssimultaneous rational approximation of irrationals

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Recurrences (11B37) Counting solutions of Diophantine equations (11D45) Linear forms in logarithms; Baker's method (11J86) Approximation to algebraic numbers (11J68)

Related Items (11)

Extension of a Diophantine triple with the property \(D(4)\) ⋮ The number of irregular Diophantine quadruples for a fixed Diophantine pair or triple ⋮ The extension of the \(D(-k)\)-triple \(\{1,k,k+1\}\) to a quadruple ⋮ Extensions of a Diophantine triple by adjoining smaller elements ⋮ Coincidence between two binary recurrent sequences of polynomials arising from Diophantine triples ⋮ On the number of extensions of a Diophantine triple ⋮ There is no Diophantine quintuple ⋮ Diophantine pairs that induce certain Diophantine triples ⋮ There are no Diophantine quadruples of Fibonacci numbers ⋮ An infinite two-parameter family of Diophantine triples ⋮ There are no Diophantine quadruples of Pell numbers

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