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Old 2008-12-17, 08:29   #2
gd_barnes
 
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May 2007
Kansas; USA

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For all bases b where b == (36 mod 37), algebraic factors on even-n combine with a numeric factor on odd-n in the following scenario:

k=m^2 and m==(6 or 31 mod 37)

Factors to:

for even-n, let n=2q:
(m*b^q-1)*(m*b^q+1)
-and-
odd-n: factor of 37


Therefore, the above applies to bases 36, 73, 110, etc. for k=6^2, 31^2, 43^2, 68^2, etc.

This pattern of factors was brought to light by me initially missing these factors for the form 36*73^n-1 and erroneously assuming that k=36 was still remaining after initial testing.


Gary

Last fiddled with by gd_barnes on 2008-12-17 at 08:37
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