On Diophantine triples containing a triangular number

2025/10/30 by Trebješanin, Marija Bliznac
#11B37 #11D09 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.26617

Abstract

A general construction yielding infinitely many families of D(m²)-triples of triangular numbers is presented. Moreover, each triple obtained from this construction contains the same triangular number T_n.

Citations

• There is no Diophantine quintuple

Related

• Diophantine triples with the property D(n) for distinct n
• Two-parameter families of uniquely extendable Diophantine triples
• Almost universal ternary sums of triangular numbers
• Finiteness results for Diophantine triples with repdigit values
• Only finitely many Tribonacci Diophantine triples exist