Quote:
Originally Posted by T.Rex
Hi,
I have no idea if this property is new. If new, I even am not sure it may be useful.
Anyway.
Let prime
and thus .
Let:
.
Mersenne.
Let:
Wagstaff.
Then:
Thus the property : . CQFD.
thus : and
thus : and thus either or .
Examples :
Probably one should only consider cases where p is a prime or a power of 2.
If , then 3 divides since only numbers can divide a Fermat number. Can be ?
If p is a prime, thus 3 cannot divide since only numbers can divide a Mersenne number, and thus 3 divides .
So, when p is a prime, when does it divide and not and viceversa ??

if p is prime, q=2*p+1 is also prime, then:
q divides M
_{p} if and only if p = 3 mod 4
q divides W
_{p} if and only if p = 1 mod 4