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Diophantine triples with the property $D(n)$ for distinct $n$
- Publication Year :
- 2022
-
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 triples with the property $D(-1)$ 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 $D(1)$.<br />Comment: Comments are welcome
- Subjects :
- Mathematics - Number Theory
11D09, 11R11
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2204.14208
- Document Type :
- Working Paper