="rcs@xmission.com" <rcs@xmission.com>
2+i is not a multiple of 2-i. They are independent prime divisors of 5. 1+i and 1-i _are_ associates; each is a multiple of the other.
OK, thanks Rich, good, I didn't goof that. Originally I wrote my message in terms of 2-i and then at the last minute screwed it up by "simplifying" to 1-i. Sorry. The point, lest it get lost in all my stupid arithmetic mistakes, was that where Havermann says that Kieran replied that
Spira's idea was that any integer can be written as a product of a
unit (±1) and positive primes
This is true if you define "positive" as Conway & Guy say that Gauss did, because then everything is indeed an associate of a unique factorization. BUT then the part with the example that leads up to the statement
where the primes 1+i and 1+2i are "positive" because both they lie
in the top right quadrant.
incorrectly (doubtless inadvertently) veers off and mis-defines "positive" as "top-right-quadrant". Specifically 1+2i *isn't* "positive" in the good sense of Gauss. Conversely you can't fully factorize 5 into "top-right-quadrant" primes exclusively. As I said, I think the overall idea is a FINE approach to defining sum of divisors, you just have to be careful to interpret Spira's "positive" as Gauss did, and not as Kieran did in the example. If I'm still unintelligible or wrong please forgive me; I will desist now.