On \(D(-1)\)-quadruples
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Publication:2248217
DOI10.5565/PUBLMAT_56212_02zbMath1354.11024OpenAlexW2042907062MaRDI QIDQ2248217
Mihai Cipu, Nicolae Ciprian Bonciocat, Maurice Mignotte
Publication date: 30 June 2014
Published in: Publicacions Matemàtiques (Search for Journal in Brave)
Full work available at URL: https://projecteuclid.org/euclid.pm/1340127807
Quadratic and bilinear Diophantine equations (11D09) Recurrences (11B37) Counting solutions of Diophantine equations (11D45) Approximation to algebraic numbers (11J68)
Related Items (9)
\(D(-1)\)-triples of the form \(\{1,b,c\}\) in the ring \(\mathbb Z[\sqrt{-t}\), \(t>0\)] ⋮ The extension of the \(D(-k)\)-pair \(\{k,k+1\}\) to a quadruple ⋮ Explicit upper bound for the average number of divisors of irreducible quadratic polynomials ⋮ There is no Diophantine D(−1)$D(-1)$‐quadruple ⋮ A polynomial variant of diophantine triples in linear recurrences ⋮ On Diophantine quintuples and \(D(-1)\)-quadruples ⋮ A Pellian equation with primes and applications to \(D(-1)\)-quadruples ⋮ \(D(-1)\) tuples in imaginary quadratic fields ⋮ Explicit upper bound for an average number of divisors of quadratic polynomials
Uses Software
Cites Work
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- On the \(D(- 1)\)-triple \(\{ 1,k^{2}+1,k^{2}+2k+2\}\) and its unique \(D(1)\)-extension
- On the extendibility of the Diophantine triple \(\{1,5,c\}\)
- On the number of Diophantine \(m\)-tuples
- Nonextendibility of \(D(-1)\)-triples of the form \(\{1,10,c\}\)
- An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
- COMPLETE SOLUTION OF A PROBLEM OF DIOPHANTUS AND EULER
- Effective solution of the D(-1)-quadruple conjecture
- THE EQUATIONS 3x2−2 = y2 AND 8x2−7 = z2
- The implicational fragment of $R$-mingle
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