Extensions of \(D(-1)\)-pairs in some imaginary quadratic fields
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Publication:6574899
Ivan Soldo, Mirela Jukić Bokun
Publication date: 19 July 2024
Published in: The New York Journal of Mathematics (Search for Journal in Brave)
Quadratic extensions (11R11) Quadratic and bilinear Diophantine equations (11D09) Counting solutions of Diophantine equations (11D45)
Cites Work
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- \(D(-1)\)-triples of the form \(\{1,b,c\}\) in the ring \(\mathbb Z[\sqrt{-t}\), \(t>0\)]
- On the \(D(- 1)\)-triple \(\{ 1,k^{2}+1,k^{2}+2k+2\}\) and its unique \(D(1)\)-extension
- Nonexistence of \(D(4)\)-quintuples
- A Pellian equation with primes and applications to \(D(-1)\)-quadruples
- THE NON-EXTENDIBILITY OF SOME PARAMETRIC FAMILIES OF D(-1)-TRIPLES
- Generalization of a problem of Diophantus
- There are only finitely many Diophantine quintuples
- There is no Diophantine quintuple
- COMPLETE SOLUTION OF A PROBLEM OF DIOPHANTUS AND EULER
- $D(-1)$-tuples in the ring $\mathbb{Z}[\sqrt{-k}$ with $k>0$]
- The non-extensibility of D(4k)-triples {1, 4k(k-1), 4k^2+1} with |k| prime
- The non-existence of \(D(-1)\)-quadruples extending certain pairs in imaginary quadratic rings
- There is no Diophantine D(−1)$D(-1)$‐quadruple
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