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

• DOI: 10.1007/s00009-022-02240-x
• Publication Date: 2022-12-11T13:03:36Z
• Authors: Kalyan Chakraborty; Shubham Gupta; Azizul Hoque
• Keywords: Pythagorean triple

Comments are welcome<br/>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/>