Re: A question about Probable Primes

In article <87d5ii7cn6.fsf@xxxxxxxxxxxxxxxxxxxx> Phil Carmody <thefatphil_demunged@xxxxxxxxxxx> writes:
> "*** T. Winter" <***.Winter@xxxxxx> writes:
> > > It is even a divisor of lambda(n) which is sometimes smaller than
> > > phi(n), i.e. when some the phi(d) of several "primitive" factors have a
> > > common factor.
> >
> > I have no idea what that lambda is.
>
> Sure you do. Carmichael lambda.

I did not, now I do. But I think it is irrelevant in the discussion.
(If I do understand it right, given the multiplicative group mod n.
It can be factored as the direct sum of a sequence of cyclic groups
pf order k_i, and lambda(n) = lcm(k_i). Clearly lambda(n) is a
divisor of phi(n), and so, indeed, an element in that groups has an
order that is a divisor of lambda(n). But for the argument it is
sufficient that it is a divisor of phi(n), which is given by
elementary group theory.)
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.

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