A new Binary Number Code and a Multiplier, based on 3 as semi-primitive root of 1 mod 2^k

Details A new Binary Number Code and a Multiplier, based on 3 as semi-primitive root of 1 mod 2^k A new Binary Number Code and a Multiplier, based on 3 as semi-primitive root of 1 mod 2^k

2001-05-03

arxiv.org/abs/math/0105029v1

Mathematics

General Mathematics

3 pages. Patent US-5923888 (13-july-1999). See also http://home.iae.nl/users/benschop/pat3star.dvi and and http://164.195.10

Scientific paper

The powers of 3 generate half of the odd residues mod 2^k (k>2), and a sign change yields the other half. In other words: 3 is a semi-primitive root of 1 mod 2^k (k>2). Hence each k-bit residue is n = +/- 3^i.2^j mod 2^k, with unique non-neg exponent pair: i<2^{k-2} and j

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