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is it known ? - divisibility for a prime p

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  • Norman Luhn
    Formula for divisibility for a prime p. Maybe it can help to findfactors of a number n ?. I have found a way to find easy a formula for each prime p. Examples:
    Message 1 of 2 , Nov 1, 2012
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      Formula for divisibility for a prime p. Maybe it can help to findfactors
      of a number n ?.

      I have found a way to find easy a formula for each prime p.

      Examples:

      p=7 ,

      7 times 1162 ?

      116-2*2=112 , 11-2*2=7 , yes !

      p=13,13=3*4+1

      13 time 72956 ?

      7295+6*4=7319 , 731+9*4=767, 76+ 7*4=104, 10+4*4=26 , yes !

      p=41 , 4-1*4=0

      41 times 11111 ?

      1111-1*4=1107, 110-7*4=82, yes !

      Today I found this. p=127 is not so easy : 127 is not x*7+12 , but we
      take 12*7-7*12

      127 times 1651 ?

      165*7-12*1=1143, 114*7-3*12=762, 76*7-12*2=508, 50*7-8*12=254,
      25*7-4*12=127 , yes !



      --

      Norman


      [Non-text portions of this message have been removed]
    • Makoto Kamada
      Method p|B*c-/+d, (c,p)=1, N=B*a+b -- p|N iff p|a*d+/-b*c Proof N*c-/+(a*d+/-b*c) =(B*a+b)*c-/+(a*d+/-b*c) =B*a*c+b*c-/+a*d-b*c =B*a*c-/+a*d =a*(B*c-/+d)
      Message 2 of 2 , Nov 2, 2012
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        Method
        p|B*c-/+d, (c,p)=1, N=B*a+b --> p|N iff p|a*d+/-b*c

        Proof
        N*c-/+(a*d+/-b*c)
        =(B*a+b)*c-/+(a*d+/-b*c)
        =B*a*c+b*c-/+a*d-b*c
        =B*a*c-/+a*d
        =a*(B*c-/+d)
        p|B*c-/+d --> p|N*c-/+(a*d+/-b*c)
        (c,p)=1 --> p|N iff p|a*d+/-b*c

        On 2012/11/02 5:26, Norman Luhn wrote:
        > 127 times 1651 ?
        > 165*7-12*1=1143, 114*7-3*12=762, 76*7-12*2=508, 50*7-8*12=254,
        > 25*7-4*12=127 , yes !

        Your choice
        127|10*12+7 --> 165*7-1*12=1143, 114*7-3*12=762, 76*7-2*12=508, 50*7-8*12=254, 25*7-4*12=127

        Shorter
        127|10*13-3 --> 165*3+1*13=508, 50*3+8*13=254, 25*3+4*13=127

        Shortest
        127|10*38+1 --> 165-1*38=127

        Reference in Japanese
        http://homepage2.nifty.com/m_kamada/di200112.htm#16

        Makoto Kamada


        On 2012/11/02 5:26, Norman Luhn wrote:
        > Formula for divisibility for a prime p. Maybe it can help to findfactors
        > of a number n ?.
        >
        > I have found a way to find easy a formula for each prime p.
        >
        > Examples:
        >
        > p=7 ,
        >
        > 7 times 1162 ?
        >
        > 116-2*2=112 , 11-2*2=7 , yes !
        >
        > p=13,13=3*4+1
        >
        > 13 time 72956 ?
        >
        > 7295+6*4=7319 , 731+9*4=767, 76+ 7*4=104, 10+4*4=26 , yes !
        >
        > p=41 , 4-1*4=0
        >
        > 41 times 11111 ?
        >
        > 1111-1*4=1107, 110-7*4=82, yes !
        >
        > Today I found this. p=127 is not so easy : 127 is not x*7+12 , but we
        > take 12*7-7*12
        >
        > 127 times 1651 ?
        >
        > 165*7-12*1=1143, 114*7-3*12=762, 76*7-12*2=508, 50*7-8*12=254,
        > 25*7-4*12=127 , yes !
        >
        >
        >
        > --
        >
        > Norman
        >
        >
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