Extensions of D(4)-pairs \a, ka\ with k∈ \7,8,10,11,12,13\

2025/11/11 by Marija Bliznac Trebješanin, Trebješanin, Marija Bliznac, Pavao Radić +1
Engineering · Mathematics · #11B37 #11D09 #11J68 #11J86 #FOS: Mathematics #Finite Group Theory Research #Mathematics and Applications #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2511.08099

openalex publication_date 2025/11/11 · openalex created_date 2025/11/13 · openalex updated_date 2026/07/28

Abstract

We study the extensibility of D(4)-pairs \a,b\, where b = ka and k ∈ \7,8,10,11,12,13\. Firstly, we show that it can be extended to a D(4)-triple with an element c, which is a member of a family of positive integers depending on a. Then, we prove that such a triple has a unique extension to a D(4)-quadruple.

Related

• On extensions of D(4)-triples by adjoining smaller elements
• The extension of the D(-k)-pair \k,k+1\ to a quadruple
• Two-parameter families of uniquely extendable Diophantine triples
• On the extensions of the Diophantine triples in Gaussian integers
• Diophantine triples with the property D(n) for distinct n