It's mostly just pointing out that in a particular extension of the integers, if we attach the square root of -5, then (1 + sqrt-5) * (1 - sqrt-5) = 2 * 3. 3 d

It's mostly just pointing out that in a particular extension of the integers, if we attach the square root of -5, then (1 + sqrt-5) * (1 - sqrt-5) = 2 * 3. 3 divides the left hand side, but it is not a divisor of either term. This is different than in the usual integers, since there are irreducible terms (not divisble by anything) that aren't prime (if they divide a product, they divide one of the factors).