A Fermat number is F(m) = 2^(2^m) + 1.

It has been shown that any factor of a Fermat number

has the form

k*2^n + 1.

with n greater than or equal to m+2

This information is at

fermatsearch.org.

if k is not odd then we have an equivalent representation

since

2*k*2^c + 1 = k*2^(c+1) + 1

I assume that mmff and other Fermat search programs

only search for odd k because the even cases will

be searched in increased exponent

Also, in the log of known Fermat factors,

http://www.prothsearch.com/fermat.html
All the k values are odd.

Regards,

Matt