19876Re: [PrimeNumbers] Many to one function which maps positive odd integers which are the sum of two squares onto the positive odd integers
- Mar 2, 2009Jack 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.
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.
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