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Re: Digest Number 1605

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  • Dick
    O.K., I ll bite ... ... if all of the prime powers in the factorizations of both x and y are such that none of the p^a==-1 mod 4, then the substitutions
    Message 1 of 2 , May 1 6:19 AM
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      O.K., I'll bite

      --- In primenumbers@yahoogroups.com, "John W. Nicholson"

      <snip>

      > Replace x with a^2+b^2, and y with c^2+d^2 then you have this
      >
      > http://mathworld.wolfram.com/SquareNumber.html
      >
      > Equation (19).

      if all of the prime powers in the factorizations of both x and y are
      such that none of the p^a==-1 mod 4, then the substitutions you
      suggest can be made, otherwise they cannot (in integers anyway)

      So the first question (after giving up on the WTF!? question) is, how
      are the x & y that cannot be integrally expressed as the sum of two
      squares to be disposed.

      The second question is how do we leap to Wiles-FLT when our x & y have
      differing exponents with severe constraints (base equals exponent of
      the other and vice versa)?


      > John W. Nicholson
      >
      > Sorry if this does not make sense, let the questions start.

      If you sense it doesn't make sense (you are quite correct in my case
      by the way), you should be able to anticipate the most likely
      questions, thus you could start answering and clarifying those without
      need of further input.

      Are you saying Mark's findings ultimately represent proof of FLT,
      Goldbach, twin prime conjecture and primes between squares?

      Curiously yours,

      Dick Boland
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