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 sinceF_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