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arXiv · 1902.00777

Diophantine quadruples with the properties $D(n_1)$ and $D(n_2)$

Andrej Dujella·Vinko Petričević
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Abstract

For a nonzero integer $n$, a set of $m$ distinct nonzero integers $\{a_1,a_2,...,a_m\}$ such that $a_ia_j+n$ is a perfect square for all $1 \leq i < j \leq m$, is called a $D(n)$-$m$-tuple. In this paper, we show that there infinitely many essentially different quadruples which are simultaneously $D(n_1)$-quadruples and $D(n_2)$-quadruples with $n_1\neq n_2$.

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Andrej Dujella, Vinko Petričević. 2019-02-09. Diophantine quadruples with the properties $D(n_1)$ and $D(n_2)$. https://doi.org/10.1007/s13398-019-00747-9

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