- --- In primenumbers@yahoogroups.com,

"Robdine" <robdine@...> wrote:

> any rational prime that can be represented by the sum

There is only rational prime of the form a^2 + b^2 that yields

> of 2 squares (a^2+b^2) will define 4 gaussian primes

precisely 4 distinct Gaussian primes, namely 2 = 1^2 + 1^2.

If a^2 + b^2 is an odd rational prime, we have

8 [sic] asociates of the Gaussian prime z = a + I*b,

since we may mulitply it and its conjugate z = a - I*b

by the 4 units I, -I, -1, 1, obtaining 8 distinct

Gaussian integers that are prime.

David - --- In primenumbers@yahoogroups.com,

"Robdine" <robdine@...> wrote:

> any rational prime that can be represented by the sum

There is only rational prime of the form a^2 + b^2 that yields

> of 2 squares (a^2+b^2) will define 4 gaussian primes

precisely 4 distinct Gaussian primes, namely 2 = 1^2 + 1^2.

If a^2 + b^2 is an odd rational prime, we have

8 [sic] asociates of the Gaussian prime z = a + I*b,

since we may mulitply it and its conjugate z = a - I*b

by the 4 units I, -I, -1, 1, obtaining 8 distinct

Gaussian integers that are prime.

David