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