Thread: I need help with a proof (by rewriting)

Hi there, because I got the comment that my descriptions weren't too good, I will copy the assignment exactly.

"9.3 F(c*(n+1)) / F(n+1) is an integer. Proof this by rewriting the quotient. F is the Fibonacci sequence so you can use F(n+2) = F(n+1) + F(n) and/or F(n+c) = F(c)F(n+1) + F(c-1)F(n)"

Well, I got stuck. I am trying and trying for over 2 hours now, but I just don't seem to see it. Can someone help me?

Originally Posted by MaryB

Hi there, because I got the comment that my descriptions weren't too good, I will copy the assignment exactly.

"9.3 F(c*(n+1)) / F(n+1) is an integer. Proof this by rewriting the quotient. F is the Fibonacci sequence so you can use F(n+2) = F(n+1) + F(n) and/or F(n+c) = F(c)F(n+1) + F(c-1)F(n)"

Well, I got stuck. I am trying and trying for over 2 hours now, but I just don't seem to see it. Can someone help me?

I guess 9.3 is just the number of the question, right?...

You can prove this by induction on using your second formula. Let be fixed. Let . Assume that where is an integer, and deduce that (where ) from the formula and the assumption.

Originally Posted by Laurent

I guess 9.3 is just the number of the question, right?...

Thank you! I get it now!
Yeah, I got the assignments by email so I just copied it directly.
Thanks again