"mikeoakes2" <mikeoakes2@...> wrote:
> > does anyone seriously believe
> > that there is a semiprime solution?
> It ought to be possible to /prove/ that there is none
That was my opinion.
The more interesting question, to my mind, is whether there
could be a non-Carmichael solution with precisely 3 prime divisors.
You found none less than 10^6 and I found none with
n <= 4638985. It is important to note that this has nothing
to do with the Moebius function, since I found a non-Carmichael
solution with 5 prime divisors, as well as several with 4.
Open question: Can there exist an integer, n, such that:
1) n is the product of 3 distinct odd primes;
2) n is not a Carmichael number;
3) there exists at least one integer q, with n > q > 0,
and V(p,q,n) = p mod n, for every integer p ?
I'm not prepared to give any more cycles to this question.
It seems to me that it needs pencil and paper, first.