## Re: Carmichael Numbers

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• ... 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

> 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.

David
• 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;
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.
>
> 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
>
> >
> > 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]
• ... 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