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Fermat's Last Theorem and modular curves over real quadratic fields

2022
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Acta Arithmetica
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There has been much recent interest in the study of the Fermat equation x n + y n = z n over number fields. Following in the footsteps of Wiles [41], we would ideally like to show that this equation has no non-trivial solutions for n ≥ 4 and x, y, z ∈ K, a number field. By a non-trivial solution, we mean xyz ̸ = 0. The study of the Fermat equation over number fields dates back to the work of Maillet in the late 19th century [13, p. 578]. Asymptotic versions of Fermat's Last Theorem over number

doi:10.4064/aa210812-2-4
fatcat:moh33whs2fdv5hpjmzpoi4j4ca