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I'd like to know how to show that, if there are no integer solutions to $a^n + b^n = c^n$ for $a, b, c, n \in Z$ and $n > 2$ then this is equivalent to either $a$ or $b = 0$ are the only rational solutions to $a^n + b^n = 1$ for $n > 2$. Not sure if this is a simple proof or not, could someone provide some pointers?

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    Note that $a=b= 0$ is not a solution to $a^n+b^n=1$2012-05-30
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    Hint: an equation like this in $\mathbb Q$ can be multiplied by something to turn it into an equation in $\mathbb Z$.2012-05-30
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    Isn't this *identical* to Fermat's Last Theorem? Or am I missing something?2012-05-30
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    @Farhad: you are not. The OP is. So you (or someone else) may want to give an answer as to how they are equivalent. (Sort of the point of a Q&A website, that is. :p )2012-05-30
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    You've got the statements slightly wrong.2012-05-30
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    See [Fermat curve](http://en.wikipedia.org/wiki/Fermat_curve).2013-11-17

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