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arXiv · 2601.19803

The extensibility of the Diophantine triple $\{2, b, c\}$

Nikola Adžaga·Alan Filipin·Ana Jurasić
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Abstract

The aim of this paper is to consider the extensibility of the Diophantine triple $\{2,b,c\}$, where $2<b<c$, and to prove that such a set cannot be extended to an irregular Diophantine quadruple. We succeed in that for some families of $c$'s (depending on $b$). As corollary, for example, we prove that for $b/2-1$ prime, all Diophantine quadruples $\{2,b,c,d\}$ with $2<b<c<d$ are regular.

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Nikola Adžaga, Alan Filipin, Ana Jurasić. 2026-01-27. The extensibility of the Diophantine triple $\{2, b, c\}$. https://doi.org/10.2478/auom-2021-0016

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