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RE: [PrimeNumbers] Squarerooting

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  • Paul Leyland
    ... Indeed. It s the quadratic residue test with modulus 9. It s subsumed in the mod 63 test I gave and it s equivalent in the other proposals. Paul
    Message 1 of 7 , Apr 4, 2001
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      > Observed heuristically, if you sum the digits of a square
      > recursively to a
      > single digit, the squares will sum to 1, 4, 7, or 9 only. For
      > example 5329-->
      > 19-->10-->1.
      >
      > Also the square sums have roots with specific sums:
      >
      > 1 squares have roots that sum to 1 or 8
      > 4 squares have roots that sum to 2 or 7
      > 7 squares have roots that sum to 4 or 5
      > 9 squares have roots that sum to 3, 6 or 9
      >
      > I think this is equivalent to one of the methods shown
      > earlier and only rules out some numbers.

      Indeed. It's the quadratic residue test with modulus 9. It's subsumed
      in the mod 63 test I gave and it's equivalent in the other proposals.


      Paul
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