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Re: [PrimeNumbers] Re: Proth's theorem extended

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  • Jack Brennen
    Bill, please explain why solutions to: 2*P*Q^2 == (P+1)*sigma(Q^2), with P,Q odd relatively prime numbers 1 exist, but why none exist when P is prime.
    Message 1 of 7 , Apr 11, 2011
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      Bill, please explain why solutions to:

      2*P*Q^2 == (P+1)*sigma(Q^2),
      with P,Q odd relatively prime numbers > 1

      exist, but why none exist when P is prime.
      Because if one exists when P is prime, that
      would give an odd perfect number.

      (To see existence, try P=22021, Q=3003.)





      On 4/11/2011 1:43 PM, leavemsg1 wrote:
      > Dimiter,
      >
      > first of all, you haven't even visited my website...
      > and second, the argument is so simple that it does NOT
      > require that someone even consider the summand portions
      > which would make the answer deficient or abundant. The
      > proof combines Euler's work w/that of Jacques Tochard's
      > from 1953; I just threaded the ideas together. (prime,
      > prime, prime; I have to mention them not to get spammed)
      > Bill
      >
      >
      > --- In primenumbers@yahoogroups.com, "Dimiter Skordev"<skordev@...> wrote:
      >>
      >> Hi,
      >>
      >> I am afraid that your idea why odd-perfect numbers don't exist would not work due to the existence of odd abundant numbers.
      >>
      >> Best regards,
      >> Dimiter
      >>
      >> --- In primenumbers@yahoogroups.com, "leavemsg1"<leavemsg1@> wrote:
      >>>
      >>> I have extended Proth's theorem.
      >>>
      >>> It can be found on my website...
      >>> www.oddperfectnumbers.com under
      >>> the Other Short Proofs heading.
      >>>
      >>> You will also find the proof for
      >>> "why odd-perfect numbers don't
      >>> exist" among others. Enjoy!
      >>>
      >>> Bill
      >>>
      >>
      >
      >
      >
      >
      > ------------------------------------
      >
      > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
      > The Prime Pages : http://www.primepages.org/
      >
      > Yahoo! Groups Links
      >
      >
      >
      >
      >
    • Dimiter Skordev
      Of course I visited Bill s website, but I thought the author gives his explanations about the non-existence of odd perfect numbers in the target page of the
      Message 2 of 7 , Apr 11, 2011
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        Of course I visited Bill's website, but I thought the author gives his explanations about the non-existence of odd perfect numbers in the target page of the link "Odd Perfect Numbers Don't
        Exist" (it turned out this is just the root page of the site). The opinion I expressed in my previous message is based on the content of the above-mentioned page.

        --- In primenumbers@yahoogroups.com, "leavemsg1" <leavemsg1@...> wrote:
        >
        > Dimiter,
        >
        > first of all, you haven't even visited my website...
        > and second, the argument is so simple that it does NOT
        > require that someone even consider the summand portions
        > which would make the answer deficient or abundant. The
        > proof combines Euler's work w/that of Jacques Tochard's
        > from 1953; I just threaded the ideas together. (prime,
        > prime, prime; I have to mention them not to get spammed)
        > Bill
        >
        >
        > --- In primenumbers@yahoogroups.com, "Dimiter Skordev" <skordev@> wrote:
        > >
        > > Hi,
        > >
        > > I am afraid that your idea why odd-perfect numbers don't exist would not work due to the existence of odd abundant numbers.
        > >
        > > Best regards,
        > > Dimiter
        > >
        > > --- In primenumbers@yahoogroups.com, "leavemsg1" <leavemsg1@> wrote:
        > > >
        > > > I have extended Proth's theorem.
        > > >
        > > > It can be found on my website...
        > > > www.oddperfectnumbers.com under
        > > > the Other Short Proofs heading.
        > > >
        > > > You will also find the proof for
        > > > "why odd-perfect numbers don't
        > > > exist" among others. Enjoy!
        > > >
        > > > Bill
        > > >
        > >
        >
      • leavemsg1
        I m am sorry for accusing you of not visiting my website. I checked my Google Analytics program on the day of your visit , and it reported that no visits came
        Message 3 of 7 , Apr 13, 2011
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          I'm am sorry for accusing you of not visiting my website.
          I checked my Google Analytics program on the day of your
          "visit", and it reported that no visits came in on that
          day; I stand corrected! www.oddperfectnumbers.com

          Bill

          --- In primenumbers@yahoogroups.com, "Dimiter Skordev" <skordev@...> wrote:
          >
          > Of course I visited Bill's website, but I thought the author gives his explanations about the non-existence of odd perfect numbers in the target page of the link "Odd Perfect Numbers Don't
          > Exist" (it turned out this is just the root page of the site). The opinion I expressed in my previous message is based on the content of the above-mentioned page.

          > > It can be found on my website...
          > > www.oddperfectnumbers.com under
          > > the Other Short Proofs heading.

          > > You will also find the proof for
          > > "why odd-perfect numbers don't
          > > exist" among others. Enjoy!
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