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19876Re: [PrimeNumbers] Many to one function which maps positive odd integers which are the sum of two squares onto the positive odd integers

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  • Kermit Rose
    Mar 2, 2009
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      Jack Brennen wrote:
      >
      > Kermit Rose wrote:
      >>
      >> Which odd positive integers are the sum of two squares?
      >>
      >> We can't say much about this.
      >>
      >
      > It is known that for an odd positive integer A, the
      > following two statements are equivalent:
      >
      > - A is a sum of two squares.
      >
      > - In the prime factorization of A, no prime of the form
      > 4x+3 appears an odd number of times.
      >
      >
      >

      Hello Jack.

      I overlooked that multiplying a sum of squares times a square also
      yields a sum of squares.

      Thus I wish to amend my Function that maps the positive odd sums of two
      squares onto the odd positive integers.

      I had not yet defined to what the function would map squares of primes
      equal to 3 mod 4.

      I extend the function to cover this case by

      F(9) = 3
      F(49) = 7

      F( q**2) = q if q is a prime equal to 3 mod 4.

      Kermit Rose
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