On Diophantine quintuples and \(D(-1)\)-quadruples

DOI10.1007/s00605-013-0571-5zbMath1347.11030OpenAlexW1984752636MaRDI QIDQ466834

Yasutsugu Fujita, Christian Elsholtz, Alan Filipin

Publication date: 31 October 2014

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-013-0571-5

zbMATH Keywords

Diophantine quadruplescounting solutions of Diophantine equationsDiophantine quintuples

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Counting solutions of Diophantine equations (11D45)

Related Items (18)

The extensibility of the \(D(\pm k)\)-triple \(\{k\mp 1,k, 4k\mp 1\}\) ⋮ \(D(-1)\)-triples of the form \(\{1,b,c\}\) in the ring \(\mathbb Z[\sqrt{-t}\), \(t>0\)] ⋮ Explicit upper bound for the average number of divisors of irreducible quadratic polynomials ⋮ Diophantine quintuples containing triples of the first kind ⋮ On the average number of divisors of reducible quadratic polynomials ⋮ There is no Diophantine D(−1)$D(-1)$‐quadruple ⋮ On Diophantine quintuple conjecture ⋮ There is no Diophantine quintuple ⋮ Two-parameter families of uniquely extendable Diophantine triples ⋮ Extension of a parametric family of Diophantine triples in Gaussian integers ⋮ A Pellian equation with primes and applications to \(D(-1)\)-quadruples ⋮ ON THE NUMBER OF DIVISORS OF ⋮ Bounds on the number of Diophantine quintuples ⋮ \(D(-1)\) tuples in imaginary quadratic fields ⋮ Further remarks on Diophantine quintuples ⋮ On a conjecture of Franušić and Jadrijević: counter-examples ⋮ Explicit upper bound for an average number of divisors of quadratic polynomials ⋮ Linear Forms in Logarithms

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