Fermat-Lucas-Carmichaels

wpolly

A positive integer is called Fermat-Lucas-Carmichael Number iff:
1) it's odd, squarefree, and have at least three distinct prime divisors;
2) for every prime $p|n$ , we have $p+1|n+1$ and $p-1|n-1$ .

construct an example of Fermat-Lucas-Carmichael number or give a proof that such numbers don't exist.

Note: those numbers are both Fermat-pseudoprime to any base and Lucas-pseudoprime to any Lucas Sequence.

**Posted:** Tue Nov 16, 2004 4:28 am

RobertuX

**Posted:** Wed Feb 16, 2005 5:36 am

_________________
RobertuX against the PEOPLE WHO try to make other people to HATES Science

rgep · Poincare Conjecture Offline Joined: 03 Jan 2005 Posts: 169

This is discussed in "Unsolved Problems in Number Theory" (3rd edition) by Richard Guy (Springer Verlag, 2004) in section A13. I believe it is still an open problem.

**Posted:** Tue Aug 23, 2005 1:43 pm