Thanks to

**R.D. Silverman** and

**jyb** for the references.

As it turns out, I've actually had both of Bent's papers in my files for over a decade.

I'd forgotten there were

*two* basic identities. Now that I'm reviewing the papers, I even vaguely recall having plowed through them at the time I originally downloaded them.

There are a few remaining algebraic details about the specific application to generalized Lucas numbers, but I'm sure I can work these out.

BTW, looking at this stuff made me think of a longstanding question: For which squarefree N > 1 does the fundamental unit of the quadratic field Q(sqrt(N)) have norm -1? It is well known, of course, that that N = 2, or N = p, a prime congruent to 1 (mod 4) fills the bill. And, of course, it is necessary that -1 be a quadratic residue of every prime factor of N. But beyond that, I'm not sure what has been found.