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Re: Formula

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  • djbroadhurst
    In primenumbers@yahoogroups.com, ... This is clearly false. Simply consider 20 = 2^2 + 4^2. David
    Message 1 of 11 , Oct 4 10:01 AM
      In primenumbers@yahoogroups.com,
      Kermit Rose <kermit@...> wrote:

      > An integer z is a sum of two squares in exactly one way
      > if and only if it is one of the following forms:
      > (1) an odd power of 2, z = 2**(2*m+1) for m > 0
      > (2) a prime equal to 1 mod 4
      > (3) the square of a prime equal to 1 mod 4 or
      > (4) z = p*h**2 where p is either 2, or an odd prime
      > equal to 1 mod 4, or the square of an odd prime equal
      > to 1 mod 4, and h has all prime factors equal to 3 mod 4.

      This is clearly false. Simply consider 20 = 2^2 + 4^2.

      David
    • djbroadhurst
      ... and then Kermit Rose mistakenly claimed ... with the irrelevant observations ... Note that 10^2 and 5^2 are not coprime. David
      Message 2 of 11 , Oct 4 10:13 AM
        I wrote:

        > An odd number N is the sum of two coprime squares in precisely
        > one way if and only if N is a prime congruent to 1 mod 4
        > or a power of such a prime.

        and then "Kermit Rose" mistakenly claimed

        > David, a Minor correction is needed here

        with the irrelevant observations

        > 2**2 + 11**2 = 5**3
        > 10**2 + 5**2 = 5**3

        Note that 10^2 and 5^2 are not coprime.

        David
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