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KConrad
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See Proposition 1 in http://www.fen.bilkent.edu.tr/~franz/ta/ta-flt.pdf and the paragraph following it. You have to adjust the terms in a potential counterexample to Fermat's Last Theorem for prime exponent $p \geq 5$ to make the Frey curve semistable. Whether or not now modularity is known in greater generality, Wiles could not handle the general case but he could handle the semistable case and that is good enough for FLT.

KConrad
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