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Old 2006-06-05, 18:46   #1
R.D. Silverman
 
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Nov 2003

746010 Posts
Question Check my arithmetic

I derived (by hand) the following polynomial for N = 2,1526L/2,218L =

2^654 + 2^600 + 2^545 - 2^436 - 2^382 - 2^327 - 2^273 - 2^218 - 2^109
+ 2^55 + 1

The polynomial is: f(x) =

x^6 + 2x^5 - 10x^4 - 20x^3 + 16x^2 - 48x + 72 with root
2^55 + 2^-54.

This polynomial sends (2z + 1/z) to (64z^12 + 64z^11 + 32z^10 - 16z^8
-16z^7 - 8z^6 - 8z^5 - 4z^4 + 2z^2 + 2z + 1)/z^6

The 12'th degree polynomial is equal to 2,1526L/2,218L with z = 2^54
(or should be if I did the arithmetic correctly)

Would someone with access to Maple/Mathematica please check this?
It was tedious to do by hand. i.e. please verify that f(2z + 1/z) equals
the 12th degree polynomial divided by z^6.
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