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


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

+r ≡ (-1)mn Ur (mod Um) and

+r ≡ (-1)mn Vr (mod Um).

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!