Abstract
We prove that for every integer n, there exist infinitely many D(n)-triples which are also D(t)-triples for \(t\in {\mathbb {Z}}\) with \(n\ne t\). We also prove that there are infinitely many \(D(-1)\)-triples in \({\mathbb {Z}}[i]\) which are also D(n)-triple in \({\mathbb {Z}}[i]\) for two distinct n’s other than \(n = -1\) and these triples are not equivalent to any triple with the property D(1).
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Acknowledgements
The authors gratefully acknowledge the anonymous referee for his/her valuable comments/suggestions that immensely improved the results as well as the presentation of the paper. The third author is supported by SERB MATRICS Project (No. MTR/2021/000762), Govt. of India.
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Chakraborty, K., Gupta, S. & Hoque, A. Diophantine Triples with the Property D(n) for Distinct n’s. Mediterr. J. Math. 20, 31 (2023). https://doi.org/10.1007/s00009-022-02240-x
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DOI: https://doi.org/10.1007/s00009-022-02240-x