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This problem came up in my conversation with a friend—not sure how basic it is, but it seems quite interesting:

Prove that if $f_n$ where $n>3$ is prime, then $n$ is prime for a Fibonacci sequence where $f_1=f_2=1.$

How can this be tackled? Thanks a bunch for any ideas.

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Basically it suffices to show, that $f_n$ is a divisibility sequence - it is shown in the link posted in the answer and also here: math.stackexchange.com/questions/60340/… –  Martin Sleziak Oct 8 '11 at 15:31
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The answer may be found at this link:

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