2022/03/07 by Imin Chen, Chen, Imin, Aisosa Efemwonkieke +3
Computer Science · Mathematics · #11D41 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2203.07870
openalex publication_date 2022/03/07 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
We prove Fermat's Last Theorem over \mathbb Q(√(5)) and \mathbb Q(√(17)) for prime exponents p ≥ 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(√(5)) is a generalization to a real quadratic base field of the one used by Chen-Siksek. For the case of \mathbb Q(√(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.