Partial Descent on Hyperelliptic Curves and the Generalized Fermat Equation
نویسندگان
چکیده
Let C : y = f(x) be a hyperelliptic curve defined over Q. Let K be a number field and suppose f factors over K as a product of irreducible polynomials f = f1f2 . . . fr. We shall define a “Selmer set” corresponding to this factorization with the property that if it is empty then C(Q) = ∅. We shall demonstrate the effectiveness of our new method by solving the generalized Fermat equation with signature (3, 4, 5), which is unassailable via the previously existing methods.
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تاریخ انتشار 2011