Thread: Proof about Fibonacci and Lucas numbers (GCD)

Hi.
How to prove that GCD(F3k, L3k)=2? and If n dosen't divide with 3 GCD(Fn, Ln)=1
Don't even know how to start that:/....Hope someone can help
Ty.

Originally Posted by aurah

Hi.
How to prove that GCD(F3k, L3k)=2? and If n dosen't divide with 3 GCD(Fn, Ln)=1
Don't even know how to start that:/....Hope someone can help
Ty.

Try to show:
a)
b) for every n.

Using these two properties you can get:
. This is either 1 or 2, since Fn and F_n-1 are coprime. So you already know that the only possible values are 1 and 2.

To show that they are equal to what you right, just nottice the pattern 0,0,1,0,0,1,.... when looking to the sequence Fn (or Ln) modulo 2.