Fibonacci number divisibility

Level 2

How many Fibonacci numbers $n$ have the property that $n\mid F_k$ where $F_k$ is the $k$ th Fibonacci number if and only if $n\mid k$ ?

The answer is 2.

1 solution

Daniel Liu
Jan 19, 2014

Simply use the property that $F_i\mid F_j$ iff $i\mid j$ . This means that we must find all $n$ such that $F_n=n$ . This is clearly when $n=1,5$ , so our answer is $\boxed{2}$ .

Fibonacci number divisibility

The answer is 2.

1 solution

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