ireducible polynomials with coefficients in ${0,-1}$
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I'm interested in the polynomials of the form $x^n -x^{n-1} - b_{n-2}x^{n-2} - cdots -b_1 x -1$ with the coefficients $b_k$ being either zero or one. The prototype is of course the Golden mean $x^2-x-1$ . Is there a known name for such polynomials? I would search for info on them, but can't figure out how to form a reasonable search query. To tighten things up: I'm interested in the ones that are irreducible with respect to one-another (are prime relative to one-another). As far as I can tell, there are the same number of these as there are irreducible polynomials over $mathbb{F}_2$ -- OEIS A001037 (should that be obvious?). As far as I can tell, they always have just one real root greater than one. I'm interested in the complex roots, too. Some of these show up in papers on "generalized gol...