2010-08-08, 18:27 | #1 |
"William"
May 2003
New Haven
3·787 Posts |
Schinzel's Aurifeuillian style factorizations?
Are there other algebraic factorizations of cyclotomic numbers or polynomials that might be helpful to projects such as Cunningham, Homogenous Cunninghams, Mishima's Cyclotomic Numbers and Odd Perfect? I recently found this abstract which says in part
Aurifeuillian Factorization ... In 1962 Schinzel gave a list of such identities that have proved useful in the Cunningham project; we believe that Schinzel identified all numbers that can be factored by such identities and we prove this if one accepts our definitionThe Schinzel paper appears to be this one.. I haven't found a free discussion of this on the web, and I'm a few weeks away from being able to access this through a university. Does anybody here know about these additional factorizations? William Edit: Found the first paper on Granville's web site. Last fiddled with by wblipp on 2010-08-08 at 18:43 |
2010-08-09, 11:04 | #2 | ||
"Gang aft agley"
Sep 2002
2·1,877 Posts |
www.cs.uwaterloo.ca/journals/JIS/VOL6/Chamberland/chamberland60.pdf
Binary BBP-Formulae for Logarithms and Generalized Gaussian-Mersenne Primes (2003) by Marc Chamberland notices some redundancies that crop up when developing BBP formulae that relate to Aurifeuillian identities. Quote:
Quote:
Last fiddled with by only_human on 2010-08-09 at 11:05 |
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2010-08-15, 20:33 | #3 |
Feb 2005
2^{2}·3^{2}·7 Posts |
Here is a couple of papers on Aurifeuillian factorizations:
http://www.artofproblemsolving.com/F...16951#p1016951 |
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