After looking at some testing done by Chris, I've added another factor to the above pattern that holds with what has already been outlined in this thread as follows:
For all bases b where b == (52 mod 53), algebraic factors on evenn combine with a numeric factor on oddn in the following scenario:
k=m^2 and m==(23 or 30 mod 53)
Factors to:
for evenn, let n=2q:
(m*b^q1)*(m*b^q+1)
and
oddn: factor of 53
Therefore, the above applies to bases 52, 105, 158, etc. for k=23^2, 30^2, 76^2, 83^2, etc.
Gary
