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Re: [PrimeNumbers] Dumb question

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  • David Litchfield
    ... Hmm. Shame. ... Well, the reason I say it s trivial is for this. Assume the number you ve been given is say 51 and we want to work out p and q. If we knew
    Message 1 of 4 , Feb 1, 2002
      > If n=pq, and x=p+q, we can say x>=2sqrt(n), and x<(n/2)+2.
      >
      > I don't think there is anything else we can infer.

      Hmm. Shame.

      >
      > >I suppose it's dumb because given the sum of the two
      > >factors it is trivial to work out the factors and so can't be done.
      >
      > If 20=p+q, what are p and q? And from this, what is pq?

      Well, the reason I say it's trivial is for this. Assume the number you've
      been given is say 51 and we want to work out p and q.

      If we knew p + q = 20 we could say

      20 / 2 = 100

      100 - 51 = 49

      sqrt(100) = 10
      sqrt(49) = 7

      10 - 7 = 3
      10 + 7 = 17

      17 * 3 = 51

      All numbers whose factors add up to give n share the same perfect squares as
      per fermat

      e.g. p + q = 20

      3 * 17 = 51, 3 + 17 = 20, 20 / 2 = 100, 100 - 51 = 49
      5 * 15 = 75, 5 + 15 = 20, 20 / 2 = 100, 100 - 75 = 25
      7 * 13 = 91, 7 + 13 = 20, 20 / 2 = 100, 100 - 91 = 9
      9 * 11 = 99, 9 + 11 = 20, 20 / 2 = 100, 100 - 99 = 1

      Cheers,
      David Litchfield
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