Ordering of nested square roots of 2 according to the Gray code
Copyright policy )Ordering of nested square roots of 2 according to the Gray code
In this paper we discuss some relations between zeros of Lucas-Lehmer polynomials and Gray code. We study nested square roots of 2 applying a "binary code" that associates bits $0$ and $1$ to $\oplus$ and $\ominus$ signs in the nested form. This gives the possibility to obtain an ordering for the zeros of Lucas-Lehmer polynomials, which assume the form of nested square roots of 2.
- Roma Tre University Italy
- Sapienza University of Rome Italy
Mathematics - Number Theory, 40A99, 11A99, 26C10, Convergence and divergence of infinite limiting processes, Real polynomials: location of zeros, nested radicals, zeros of Chebyshev polynomials, continued radicals, FOS: Mathematics, Number Theory (math.NT), continued roots, Elementary number theory, nested radicals; continued radicals; continued roots; Gray code; zeros of Chebyshev polynomials, Gray code
Mathematics - Number Theory, 40A99, 11A99, 26C10, Convergence and divergence of infinite limiting processes, Real polynomials: location of zeros, nested radicals, zeros of Chebyshev polynomials, continued radicals, FOS: Mathematics, Number Theory (math.NT), continued roots, Elementary number theory, nested radicals; continued radicals; continued roots; Gray code; zeros of Chebyshev polynomials, Gray code
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