On Triangular Diophantine SetsMPIM

by Alan Filipin (MPIM)

Wednesday Feb 18, 2026, 2:30 PM → 3:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Number theory lunch seminar

Let $m\geq 2$ be an integer. For integer $n \neq 0$, we introduce one variation of Diophantine problem, when we call the set of $m$ distinct
positive integers a Triangular $D(n)$-$m$-tuple if any product of its two  distinct elements increased by $n$ is a triangular number. As usual in similar problems, the question of interest asks the cardinality of such Triangular Diophantine sets. In this talk we will present some work on the extendibility of various Triagular triples and give some ideas for future search. It is joint work with L. Szalay, Y. Fujita and A. Jurasić.