MHB Generalized Fibonacci and Lucas Numbers.

[meow91006]

[h=2][/h]

Can you help me prove this theorem regarding Fibonacci and Lucas numbers?

Theorem.

Let m,r ϵ Z and n be non-zero integer. Then

U_2mn+r ≡ (-1)^mn U_r (mod U_m) and

V_2mn+r ≡ (-1)^mn V_r (mod U_m).Im not that good at proving. This type of congruence is much harder than what I read in our book, but I badly need the proof for this one, even just this one, to understand better Fiboancci and Lucas numbers.

I'd be glad to hear from you soon.
Thank you very much!​

 

[CaptainBlack]

Can you help me prove this theorem regarding Fibonacci and Lucas numbers?

Theorem.

Let m,r ϵ Z and n be non-zero integer. Then

U_2mn+r ≡ (-1)^mn U_r (mod U_m) and

V_2mn+r ≡ (-1)^mn V_r (mod U_m).Im not that good at proving. This type of congruence is much harder than what I read in our book, but I badly need the proof for this one, even just this one, to understand better Fiboancci and Lucas numbers.

I'd be glad to hear from you soon.
Thank you very much!​

That is not a question as it stands, please post the full question.

CB