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Proth's theorem extended

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  • leavemsg1
    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
    Message 1 of 7 , Apr 9, 2011
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      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
    • Dimiter Skordev
      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
      Message 2 of 7 , Apr 11, 2011
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        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
        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
        Message 3 of 7 , Apr 11, 2011
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          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
          > >
          >
        • 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 4 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 5 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 6 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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