Proof by Induction Homework: Proving F_n|F_{kn}

[hangainlover]

Homework Statement

I have proved the first one and I am trying to do the second using the result from part 1)

Homework Equations

$F_1=1, F_2=2, F_n=F_{n-1}+F_{n-2}$

The Attempt at a Solution

base case: $F_1|F_k$ since$F_1=1$

Assume it works for n, $F_n|F_{kn}$
show $F_{n+1}|F_{kn+k}$

Well, using the part 1)
$F_{kn+k}=F_kF_{kn+1}+F_{k-1}F_{kn}$

That's as far as i could go..

 

[hangainlover]

I have uplloaded the problem statement in the attachment
sorry i forgot to mention that