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Re: Cyclotomic polynomial puzzles

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  • David Broadhurst
    ... Perhaps because the mods have set that as the on-line default? I tried to reply, but maybe I forgot that trap. There is no way of telling, since the
    Message 1 of 43 , May 10, 2009
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      --- In primenumbers@yahoogroups.com,
      Phil Carmody <thefatphil@...> asked:

      > Why's everyone only replying off-list?

      Perhaps because the mods have set that as the on-line default?
      I tried to reply, but maybe I forgot that trap.
      There is no way of telling, since the default
      reply is not even copied to oneself.

      Here goes again (sorry if it eventually appears twice):

      > 3a) Can you categorise p,q,r such that Phi(pqr) only has
      > coefficients in {-1,0,1}?
      >  b) Can you find a bigger pqr with that property than
      > anyone else?

      pqr=
      103534127524074104115541098969958708089926902711923091490097\
      001545810093892338679248846099390229911806167096020172161339\
      248099921117956336949559455817976090558652472327237037907245\
      079673380295270552412505821551314360478060083799787164050405\
      497609391864910896620579324752947949306589953853514558460087\
      480667962113549945569489945478510973601172041512307421653813\
      8676796204064794079723241321918976844647423

      has a cyclotomic polynomial that is easily proven to be flat,
      once you have factorized pqr into its 3 constituent primes.
      Yet I believe that I am the only person in the world
      who can actually prove that Phi(pqr) is indeed flat,
      if the CIA has not yet spooked my hard drive.

      Proof:

      print(concat(isprime([p,q,r]),[pqr==p*q*r,r>q,q>p,Mod(r,q*p)^2==1]))
      [1, 1, 1, 1, 1, 1, 1]

      David (with thanks to Nathan)
    • djbroadhurst
      ... On who regularly publishes, in mathematical journals, articles that do not derive principally from other subjects, such as physics. David (pleading not
      Message 43 of 43 , May 23, 2013
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        --- In primenumbers@yahoogroups.com,
        whygee@... asked:

        > What's a "proper mathematician" ?

        On who regularly publishes, in mathematical journals,
        articles that do not derive principally from other subjects,
        such as physics.

        David (pleading not guilty)
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