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Re: Conjecture Prime
Posted: Jun 26, 2009 1:55 PM

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Musatov wrote:
pubkeybreaker wrote:
> On Jun 25, 8:53 am, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> > In article <d0f06d18-0844-4c10-9f84-d20bfd704...@z20g2000prh.googlegroups.com> Musatov <marty.musa...@gmail.com> writes:
> > > On Jun 24, 10:39 pm, ab <hobk...@gmail.com> wrote:
> > ...
> > > > > > > The equation and opeation must be written as follows:
> > > > > > > (N*N)((N*N)+2)-1
> > ...
> > > > > Now when I say it produces prime number or composites, I am saying it
> > > > > produces ALL primes, except when it does not
> > > > > it will produce at least two prime factors from the exception
> > > > > COMPOSITES.
> > > >
> > > > unique prime factors? or do you allow a prime repeated, for example
> > > > (N*N)((N*N)+2) - 1 = p^2
> > >
> > > It's not up to me, I am stating factual discovery. Or at least is is
> > > my intent. I cannot see how multiplying to even numbers with a
> > > difference of two will allow for a composite square with a identical
> > > prime factors.
> > >
> > > Do you?
> >
> > N = 46, (N*N)(N*N+2)-1 = 4481687 = 7 * 7 * 91463
>
> Indeed. Just apply Hensel's lemma to a solution mod 7. It will
> also have solutions mod 7^3, 7^4, ........
>
> Note also that n^4 +2n^2-1 will be divisible by 7^2 for n = 46 +
> 49k
> for all integer k. Note the solution at n = -3. It also has
> solutions at
> 3 + 49k for all integer k...... (note that the function is even)

The intent is to create a useful function, not win a Field's award.
Thanks for the information and feedback.

--
Musatov