It's good that none of us knows what we're doing, so we all feel inadequate together, huh?
I suppose all it really means is that the a(n-1) thing works for more than just the n value we're looking for. So if you have a c with more than two n values (i.e. it has more than two prime factors plus one and itself), all of them will do that thing. But we could have figured that out by just sort of thinking about it outside of the context of semiprimes and testing it. Most of these rules do apply to more than just semiprimes. This is what happens when I do math when I should be asleep. I forget that the things I find are things I already know to be true.