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If the Taniyama-Shimura Conjecture holds for all semistable Elliptic Curves, then Fermat's Last Theorem is true. Before its proof by Ribet in 1986, the theorem had been called the epsilon conjecture. It had its roots in a surprising result of G. Frey.
See also Elliptic Curve, Fermat's Last Theorem, Modular Form, Modular Function, Taniyama-Shimura Conjecture