7 papers
A new Binary Number Code and a Multiplier, based on 3 as semi-primitive root of 1 mod 2^k
N. F. Benschop
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…
Symmetric Logic Synthesis with Phase Assignment
N. F. Benschop
Decomposition of any Boolean Function BF_n of n binary inputs into an optimal inverter coupled network of Symmetric Boolean functions SF_k (k \leq n) is described. Each SF componen…
Finite Semigroups of Constant Rank, and the five Basic State Machine types
N. F. Benschop
Constant Rank (CR) state machines play an important role in the general structure theory of Finite State Machines. A machine is of constant rank if each input and input-sequence ma…
Powersums representing residues mod p^k, from Fermat to Waring
N. F. Benschop
The ring Z_k(+,.) mod p^k with prime power modulus (prime p>2) is analysed. Its cyclic group G_k of units has order (p-1)p^{k-1}, and all p-th power n^p residues form a subgroup F_…
On Fermat's marginal note: a suggestion
N. F. Benschop
A suggestion is put forward regarding a partial proof of FLT(case1), which is elegant and simple enough to have caused Fermat's enthusiastic remark in the margin of his Bachet edit…
On primitive roots of unity, divisors of p+/-1, Wieferich primes, and quadratic analysis mod p^3
N. F. Benschop
Primitive roots of 1 mod p^k (k>2 and odd prime p) are sought, in cyclic units group G_k = A_k B_k mod p^k, coprime to p, of order (p-1)p^{k-1}. 'Core' subgroup A_k has order p-1 i…