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

Theorem.

Letm,rϵ Z andnbe non-zero integer. Then

U_{2mn}_{+r}≡ (-1)^{mn}U(mod_{r}U) and_{m}

V_{2mn}_{+r}≡ (-1)^{mn}V(mod_{r}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!