Thread: Polynomial
View Single Post
Old 2005-09-16, 12:28   #9
R.D. Silverman
 
R.D. Silverman's Avatar
 
Nov 2003

22×5×373 Posts
Default

Quote:
Originally Posted by kubus
Here are my calculations.

We can represent 2,1378M as y13+xy6+1,
where y=253 and x=227.

2,26L is y-x+1.

Now dividing y13+xy6+1 by y-x+1 and taking advantage of an equality x2=2y we get
A(y)+xB(y), where
A(y)=y12+y11-y10-y9+y8+y7-y6+y5+y4-y3-y2+y+1
B(y)=y11-y9+y7+y4-y2+1

A(y) and B(y) are symmetrical so we reduce the coeffs by representing poly with root z=227+2-26. We get 12th degree polynomial and in fact this is trilliwig's formula %9.

wblipp, I don't understand how to "pull out" 2,2M, too.

kubus

Yes, I was looking for formula %9. I was hoping that it might be
symmetric. It is not, but I thought that if it isn't, it might have a
representation as a sextic not in (z+1/z), but rather [with Z = 2^53]
in (z + 2/z). It seems that it does, but the constant is much too large.
Perhaps we might try a sextic in (z + k/z) for some other value of k?
R.D. Silverman is offline