Newsgroups: rec.puzzles
From: hoey@aic.nrl.navy.mil (Dan Hoey)
Date: 1996/01/26
Subject: Re: SPOILER to math puzzle 6

dcarr...@oucsace.cs.ohiou.edu (Dana Carroll) writes:

: >Two different primes, the product of which is divisble by the sum?

: ...The definition of primeness that most people accept only applies
: to the positive integers, but in fact the mathematical definition of
: primeness applies in any UFD.  (Actually, we have irreducibles and
: primes, which are not necessarily the same in a UFD, but are
: equivalent in a PID).  Thus, 3 and -2 satisfy the problem, as well
: as 2 and -3.  But these are the only ones....

Yes, but 3 and -2 are the same two primes as -3 and 2--they generate
the same ideal.  So there's only one solution.

Dan
Hoey@AIC.NRL.Navy.Mil