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Topic: Conjecture Prime
Replies: 33   Last Post: Apr 26, 2013 7:21 AM

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Pubkeybreaker

Posts: 1,380
Registered: 2/12/07
Re: Conjecture Prime
Posted: Jun 25, 2009 10:06 AM
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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)




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