论文标题
Fermat的最后一个定理$ {\ Mathbb Q}（\ sqrt {5}）$和$ {\ Mathbb Q}（\ sqrt {17}）$
Fermat's Last Theorem over ${\mathbb Q}(\sqrt{5})$ and ${\mathbb Q}(\sqrt{17})$
论文作者
论文摘要
我们证明了Fermat在$ {\ Mathbb Q}（\ sqrt {5}）$和$ {\ Mathbb Q}（\ sqrt Q}（\ sqrt {17}）$的质量指数$ p \ ge 5 $ 5 $中的某些一致性$ 48 $中，由Moduly of Modular Quare quare quare-quartimal quare-ge 5 $，互惠限制。用于治疗$ {\ mathbb q}情况的互惠约束（\ sqrt {5}）$是对Chen-Siksek使用的一个真实二次基地的概括。对于$ {\ Mathbb Q}（\ sqrt {17}）$，这是不足的，我们使用Hilbert符号从理性字段中概括了Bennett-Chen-dahmen-yazdani的相互约束，以便某些实际的Quadratic字段。
We prove Fermat's Last Theorem over ${\mathbb Q}(\sqrt{5})$ and ${\mathbb Q}(\sqrt{17})$ for prime exponents $p \ge 5$ in certain congruence classes modulo $48$ by using a combination of the modular method and Brauer-Manin obstructions explicitly given by quadratic reciprocity constraints. The reciprocity constraint used to treat the case of ${\mathbb Q}(\sqrt{5})$ is a generalization to a real quadratic base field of the one used by Chen-Siksek. For the case of ${\mathbb Q}(\sqrt{17})$, this is insufficient, and we generalize a reciprocity constraint of Bennett-Chen-Dahmen-Yazdani using Hilbert symbols from the rational field to certain real quadratic fields.
