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This question already has an answer here:

Fermat numbers are shown by: $F_m = 2^{2^m} + 1$.

How can I prove that for any $m ≠ n$, I can have $(F_m, F_n) = 1$, or coprime?

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marked as duplicate by Thomas Andrews, Venus, Namaste, Dietrich Burde, quid Jan 23 '15 at 15:34

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