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Old 2008-12-19, 20:19   #4
gd_barnes
 
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May 2007
Kansas; USA

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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 even-n combine with a numeric factor on odd-n in the following scenario:

k=m^2 and m==(23 or 30 mod 53)

Factors to:

for even-n, let n=2q:
(m*b^q-1)*(m*b^q+1)
-and-
odd-n: 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
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