Diophantine Triples with the Property D(n) for Distinct n’s

We prove that for every integer n , there exist infinitely many D ( n )-triples which are also D ( t )-triples for t ∈ Z with n ≠ t . We also prove that there are infinitely many D ( - 1 ) -triples in Z [ i ] which are also D ( n )-triple in Z [ i ] for two distinct n ’s other than n = - 1 and these...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 20; no. 1
Main Authors Chakraborty, Kalyan, Gupta, Shubham, Hoque, Azizul
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2023
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Pellian equations
11R11
11D09
Diophantine quadruples
Quadratic fields
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Summary:We prove that for every integer n , there exist infinitely many D ( n )-triples which are also D ( t )-triples for t ∈ Z with n ≠ t . We also prove that there are infinitely many D ( - 1 ) -triples in Z [ i ] which are also D ( n )-triple in Z [ i ] for two distinct n ’s other than n = - 1 and these triples are not equivalent to any triple with the property D (1).
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-022-02240-x