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arXiv · 1504.04892

Sur l'\'equation $X^2-\varepsilon_2\varepsilon_{p_1p_2}\varepsilon_{2p_1p_2}=0$

Abdelmalek Azizi·Abdelkader Zekhnini·Mohammed Taous
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Abstract

Let $p_1\equiv p_2\equiv5 \pmod8$ be prime numbers such that $\left(\frac{p_1}{p_2}\right)=-1$. Let $\mathbb{L}=Q(\sqrt2, \sqrt{p_1p_2})$ Our goal is to resolve the equation $X^2-\varepsilon_2\varepsilon_{p_1p_2}\varepsilon_{2p_1p_2}=0$ in $\mathbb{L}$, where $\varepsilon_j$ are fundamental units of real quadratic subfields of $Q(\sqrt2, \sqrt{p_1p_2})$.

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Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous. 2015-04-19. Sur l'\'equation $X^2-\varepsilon_2\varepsilon_{p_1p_2}\varepsilon_{2p_1p_2}=0$. https://arxiv.org/abs/1504.04892

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