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    $\begingroup$ mathteacherctk.com/blog/2010/09/… $\endgroup$ Commented Aug 26, 2013 at 15:11
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    $\begingroup$ @Koundinya Vajjha: so, FLT would be just as useful if Wiles had finally disproved it! $\endgroup$ Commented Aug 26, 2013 at 16:00
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    $\begingroup$ It has been used to good effect to prove the irrationality of $2^{1/n}$ here: mathoverflow.net/a/42519/8430 (sorry, couldn't resist this joke) $\endgroup$ Commented Aug 26, 2013 at 16:19
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    $\begingroup$ Alex B.'s answer is certainly a great application of the $p=7$ case, proved by Lamé in 1839. I would be interested to know if there is a substantial application for which pre-Wiles work did not suffice. $\endgroup$ Commented Aug 26, 2013 at 23:16
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    $\begingroup$ @suvrit, that application is the same as in Carlo's comment. $\endgroup$ Commented Aug 26, 2013 at 23:44