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Conjecture Question.

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  • Markus Frind
    Is there a conjecture that states that every even number can be expressed as the sum of powers of 2 ? 42 = 32 + 8 + 2 Powers of 2 that weren t used to get to
    Message 1 of 4 , Jun 1, 2002
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      Is there a conjecture that states that every even number can be expressed
      as the sum of powers of 2 ?

      42 = 32 + 8 + 2

      Powers of 2 that weren't used to get to 42..
      4,16

      The next power of 2 over 42 is 64. If we go 64 - 16 -4 we should
      get 44 ( we always end up with the number +2)

      134 = 2+4+128

      powers that weren't used...
      136 = 256 - (16+32+64+8)


      Markus
    • Markus Frind
      Never mind, I suppose we can call this the binary number system!
      Message 2 of 4 , Jun 1, 2002
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        Never mind, I suppose we can call this the binary number system!

        At 12:12 AM 6/1/2002 -0700, Markus Frind wrote:
        >Is there a conjecture that states that every even number can be expressed
        >as the sum of powers of 2 ?
        >
        >42 = 32 + 8 + 2
        >
        >Powers of 2 that weren't used to get to 42..
        >4,16
        >
        >The next power of 2 over 42 is 64. If we go 64 - 16 -4 we should
        >get 44 ( we always end up with the number +2)
        >
        >134 = 2+4+128
        >
        >powers that weren't used...
        >136 = 256 - (16+32+64+8)
        >
        >
        >Markus
        >
        >
        >
        >Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
        >The Prime Pages : http://www.primepages.org
        >
        >
        >
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      • Satoshi TOMABECHI
        ... It is an obvious fact. It is not a conjecture. Satoshi Tomabechi
        Message 3 of 4 , Jun 1, 2002
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          Markus Frind wrote:
          > Is there a conjecture that states that every even number can be expressed
          > as the sum of powers of 2 ?

          It is an obvious fact. It is not a conjecture.

          Satoshi Tomabechi
        • Ben Newsam
          In message , Markus Frind writes ... Well, yes. If you used bit 0 as well, you
          Message 4 of 4 , Jun 1, 2002
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            In message <5.0.0.25.2.20020531235709.033ebba0@...>, Markus
            Frind <flames@...> writes
            >Is there a conjecture that states that every even number can be expressed
            >as the sum of powers of 2 ?
            >
            >42 = 32 + 8 + 2
            >
            >Powers of 2 that weren't used to get to 42..
            >4,16
            >
            >The next power of 2 over 42 is 64. If we go 64 - 16 -4 we should
            >get 44 ( we always end up with the number +2)
            >
            >134 = 2+4+128
            >
            >powers that weren't used...
            >136 = 256 - (16+32+64+8)

            Well, yes. If you used bit 0 as well, you would find that two's
            complement arithmetic worked properly without being out by two.
            --
            Ben
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