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arXiv · 2403.17959

Rational Diophantine sextuples with strong pair

Andrej Dujella·Matija Kazalicki·Vinko Petričević
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Abstract

A set of $m$ distinct nonzero rationals $\{a_1, a_2,\ldots, a_m\}$ such that $a_i a_j+1$ is a perfect square for all $1\le i <j \le m$, is called a rational Diophantine $m$-tuple. If in addition, $a_i^2+1$ is a perfect square for $1\le i\le m$, then we say the $m$-tuple is strong. In this paper, we construct infinite families of rational Diophantine sextuples containing a strong Diophantine pair.

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Andrej Dujella, Matija Kazalicki, Vinko Petričević. 2024-03-12. Rational Diophantine sextuples with strong pair. https://arxiv.org/abs/2403.17959

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