Here's some more on Greg Whitehead's solution to the 80% Dozenegger http://thaneplambeck.typepad.com/thaneplambeck/ Scroll down past the blackboard photo -- but only if you want to see a photo of the solution ! Thane On Wed, Sep 24, 2008 at 11:49 PM, <rwg@sdf.lonestar.org> wrote:
rwg>A couple of days ago Mathematica disgorged a resultant for p{4,6,9}, a geometric progression with a presumably simple polynomial, but got > 2000 terms, with thousand-digit coefficients, and square-free! Needless to say, the factorization is still in progress.
Joke's on me. Saddam XP forced me to terminate the factorization (and then pay for the bullet) when "an initialization failed", without even letting me look in the window. But I was then able to find the various factors of p{3,6,9}/p{2,3,4}, and in a complete reversal of tradition, the answer turned out to be the *largest*,
p{4,6,9} = 4096*eta(q^6)^1296 - <<878>> + 296975826110677186501810694400299649164810446749391313181000047331065773408181565393812635137798905081215065695126808741771033488065035979225233690130907136*eta(q^4)^288*eta(q^6)^144*eta(q^9)^864.
rwg> The shapes of these polynomials are surprising. --rwg PS, Greg Whitehead found an unintended but very legitimate solution to Thane's 80% filled Arnold Dozenegger. The 82% model remains unsolved (except by "codesigner" Emma Cohen), despite a furious and prolonged attack by Cheny Xu. (Who keeps sending perplexing photos of bogus solutions that I find physically unfeasible.) There are presumably no unintended solutions.
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-- Thane Plambeck tplambeck@gmail.com http://www.plambeck.org/ehome.htm