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Re: Ruler, compass and prime power

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  • mikeoakes2
    ... N is divisible by every prime p = 1 (mod 4) and p
    Message 1 of 33 , Oct 31, 2011
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      --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
      >
      > Rider [to satisfy Mike]: For N =
      > 549331419852485793001165813448560300688932146594014566096\
      > 201737173918077841916892020858108961291281080905964542945
      > construct /all/ of the right angle triangles whose square on the
      > hypotenuse is N^3 and whose other two sides have integral lengths.
      > For /each/ of these, trisect an acute angle of the triangle
      > using ruler and compass only.

      N is divisible by every prime p = 1 (mod 4) and p<=137.
      The quotient is composite, but too hard for pari-GP to factorise (as yet).
      If accomplished, it would then be straightforward to construct all the relevant right-angled triangles, by partitioning the factors.

      Mike
    • Ben Buhrow
      ... I saw that, thanks David! Since this is a list dedicated to primes, I ll also just mention briefly that yafu has one of the fastest sieve of Eratosthenes
      Message 33 of 33 , Nov 8, 2011
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        --- In primenumbers@yahoogroups.com, David Cleaver <wraithx@...> wrote:
        >
        >

        >
        > Ben, I've been trying to tell them how awesome Yafu is! You can see my message
        > here:
        > http://tech.groups.yahoo.com/group/primenumbers/message/23598
        >
        > If anyone needs any factoring utilities, yafu should be first on the list. Then
        > some combination of yafu/msieve/ggnfs to factor larger numbers. I tried to
        > spell it all out in the above post. Hopefully I didn't misrepresent any info
        > about yafu. Please correct me if I was wrong. If anyone has any questions,
        > feel free to ask on this list.
        >
        > -David C.
        >
        > P.S. For full disclosure, I helped contribute a small amount of code to yafu. :)
        >

        I saw that, thanks David!

        Since this is a list dedicated to primes, I'll also just mention briefly that yafu has one of the fastest sieve of Eratosthenes implementations I'm aware of, for generating lists of primes in arbitrary ranges up to 10^19. Maybe that is useful to folks here too.

        cheers,
        - ben.
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