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arXiv · 1312.5241

Non-extensibility of the pair $\{1, 3\}$ to a Diophantine quintuple in $\mathbb{Z}\left[\sqrt{-d}\right]$

Zrinka Franušić·Dijana Kreso
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Abstract

We show that the Diophantine pair $\{1, 3\}$ can not be extended to a Diophantine quintuple in $\mathbb{Z}\left[\sqrt{-2}\right]$. This result completes the work of the first author and establishes non-extensibility of the Diophantine pair $\{1, 3\}$ to a Diophantine quintuple in $\mathbb{Z}\left[\sqrt{-d}\right]$ for all $d\in \mathbb{N}$.

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Zrinka Franušić, Dijana Kreso. 2013-12-18. Non-extensibility of the pair $\{1, 3\}$ to a Diophantine quintuple in $\mathbb{Z}\left[\sqrt{-d}\right]$. https://arxiv.org/abs/1312.5241

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