Re: No multiples of 5 in the Lucas sequence

Am 03.12.2005 13:14 schrieb Gottfried Helms:
> Some additional remarks:
>
> Still it is much interesting to me, that the order can be greater than
> p, and also it is of interest, to which extent this can happen?
>

It seems, that primefactors of the form +-1 (mod 5)
of the fibonacci-sequence (function f(n))
behave "well", thus their cyclic subgroup-order
is divisor of p-1= phi(p),

and primefactors of the form +-2 (mod 5) have an order
of a divisor of p+1 = phi(p)+2

and the single primefactor 0 (mod 5) has itself as the order.

Gottfried Helms
.

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