Diophantine triples with the property D(n) for distinct n

2022/04/29 by Kalyan Chakraborty, Shubham Gupta, Chakraborty, Kalyan +3
Mathematics · #Mathematical Dynamics and Fractals #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.2204.14208

Abstract

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 triples with the property D(-1) 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).

Related

• On Diophantine triples containing a triangular number
• Only finitely many Tribonacci Diophantine triples exist
• Finiteness results for Diophantine triples with repdigit values
• Diophantine quintuples containing triples of the first kind
• Two-parameter families of uniquely extendable Diophantine triples