Thread: What's next?
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Old 2005-05-13, 06:38   #17
frmky
 
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Jul 2003
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Quote:
Originally Posted by R.D. Silverman
2^760 + 1 = x^5 + 1 with x = 2^152. But x^5+1 =
(x+1)(x^4-x^3+x^2-x+1)

So just use x - M and x^4-x^3+x^2-x+1 with M = 2^152

It is best NOT to convert the reciprocal quartiic into a quadratic in (x+1/x)
because doing so blows up the coefficients on the linear side by too much.
How about M=2^76+2^-76 and the polys x^4-5x^2+5, 2^76x-2^152-1? Does eliminating the odd powers in the polynomial help? Does increasing the linear coefficient of the linear polynomial hurt much? Just curious...

Greg
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