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Re: Carmichael Numbers

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  • David Broadhurst
    ... How many mistakes can be packed into 7 words? 1) Deveraj has no Thoerem. 2) Devaraj has no theorem, either. 3) Pomerance (not Pomernce) and 4) Alekseyev
    Message 1 of 11 , Apr 4, 2009
      --- In primenumbers@yahoogroups.com,
      Devaraj Kandadai <dkandadai@...> wrote:

      > corollary of the Devaraj-Pomernce-Maxal Thoerem

      How many mistakes can be packed into 7 words?

      1) Deveraj has no Thoerem.
      2) Devaraj has no theorem, either.
      3) Pomerance (not Pomernce) and
      4) Alekseyev (not Maxal) showed that
      5) merely half of a conjecture by Deveraj holds,
      6) while the other half is patently false
      7) and hence can have no corollary.

      Any advance on 7 mistakes?

      David
    • Devaraj Kandadai
      Dear Maxmilian, Let me clarify; A 104016 is the sequence of Devaraj Numbers which are also Carmichael Numbers and A 104017 is that of Devaraj Numbers which
      Message 2 of 11 , Apr 4, 2009
        Dear Maxmilian,
        Let me clarify;
        A 104016 is the sequence of Devaraj Numbers
        which are also Carmichael
        Numbers and A 104017 is that of Devaraj Numbers which are NOT CNs. Both
        display a property of
        Let me clarify; A 104016 represents Devaraj numbers which are CNs and
        A104017 represents DNs which are not CNs. best illustrated by following
        numerical examples

        Let us take 561, the smallest CN.

        561=3*11*17;
        My conjecture about this is that 2*560/10*16 is
        an integer ( and so it is =7).

        Now let us take the smallest in the seq A 104017 viz 11305=5*7*17*19

        My conjecture: 4*11304*11304/6*16*18 is an integer and so it is.

        As regards my site if it is not accessible I wd be only too happy to send
        the relevant file as an attachment/

        Trust I have made myself clear.
        A.K.Devaraj

        On Sat, Apr 4, 2009 at 11:34 AM, Maximilian Hasler <
        maximilian.hasler@...> wrote:

        > It seems impossible to access http://www.crorepatibaniye.com/.<http://www.crorepatibaniye.com/>
        > The last update seen by web.archive of /any/ page on that site dates back
        > to Nov.2007.
        > The latest version of your "theorem" which I can access via web.archive is
        >
        > http://web.archive.org/web/20070111140456/http://www.crorepatibaniye.com/failurefunctions/conjecture2.asp
        > which has been *disproved*: sequence
        > http://www.research.att.com/~njas/sequences/A104017
        > lists the first three lines of counter-examples.
        >
        > Given the moderate number of Mersenne primes we know and the rate at which
        > this knowledge increases, you are quite safe from a counter-example against
        > your new Conjecture (re-stated as: "the prime factors of a Carmichael Number
        > cannot all be Mersenne").
        >
        > Maximilian
        >
        > --- In primenumbers@yahoogroups.com <primenumbers%40yahoogroups.com>,
        > Devaraj Kandadai <dkandadai@...> wrote:
        > >
        > > I am inclined to believe that this is a corollary of the
        > > Devaraj-Pomernce-Maxal Thoerem (see
        > > www.crorepatibaniye.com/failurefunctions).
        > > A.K. Devaraj
        > >
        > > On Thu, Apr 2, 2009 at 4:37 PM, Devaraj Kandadai <dkandadai@...>wrote:
        > >
        > > > My conjecture pertaining to Carmichael Numbers was proved by Pomerance
        > > > and Maxal(see www.crorepatibaniye.com/failurefunctions). Another
        > > > conjecture:
        > > >
        > > > All the factors of a Carmichael Number cannot be Mersenne.
        > > >
        > > > You are hereby invited to prove/disprove the above.
        > > >
        > > > A.K.Devaraj
        >
        >
        >


        [Non-text portions of this message have been removed]
      • Maximilian Hasler
        ... As far as I understood, the D-numbers are /defined/ as those for which this is an integer; your conjecture says that this is a CN, but it isn t. Maximilian
        Message 3 of 11 , Apr 5, 2009
          --- In primenumbers@yahoogroups.com, Devaraj Kandadai wrote:

          > Now let us take the smallest in the seq A 104017 viz 11305=5*7*17*19
          >
          > My conjecture: 4*11304*11304/6*16*18 is an integer and so it is.

          As far as I understood, the D-numbers are /defined/ as those for which this is an integer; your conjecture says that this is a CN, but it isn't.

          Maximilian

          PS: the posts 2e4 and 2e4-1 are empty since you cannot send attachments. But we have the Pomerance-Alekseyev proof at http://www.mersenneforum.org/showpost.php?p=55271
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