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Number Theory Generalized Fibonacci and Lucas Numbers.

meow91006

New member
Aug 6, 2012
1
[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

U2mn
+r ≡ (-1)mn Ur (mod Um) and

V2mn
+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!
 

CaptainBlack

Well-known member
Jan 26, 2012
890
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

U2mn
+r ≡ (-1)mn Ur (mod Um) and

V2mn
+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!
That is not a question as it stands, please post the full question.

CB