Titlebook: Associative Digital Network Theory; An Associative Algeb Nico F. Benschop Book Apr 2009Latest edition Springer Science+Business Media B.V.

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https://doi.org/10.1007/3-540-36135-9idues mod .. with ‘carry’ .<.. of weight .. yields a Euclidean prime sieve for integers. Failure of Goldbach’s Conjecture (.) for some 2. contradicts .(.) for some ., yielding .: Each 2.>4 is the sum of two odd primes.

Consequence

MERIT

Simple Semigroups and the Five Basic Machines,ch input and input-sequence maps the state set onto the same number of next states. CR-machines are analysed by their sequential closure (semigroup), which is shown to be a ., that is: a semi-direct product . |>(.×.) of a left- and a right-copy semigroup, and a group. So in general a CR-machine is a

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REP

,Fermat’s Small Theorem Extended to ,,mod ,,,. are shown to have distinct .. mod .., and divisors . of .−1 (resp. .+1) with different primesets have distinct .. mod ... Moreover 2.≢2  mod .. for prime ., related to . primes (Wieferich in J. Reine Angew. Math. 136:293–302, .) and . case. for integers (Chap. 8). .: Some .|.±1 is semi primitive r

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,Additive Structure of ,(.) mod ,, (Squarefree) and Goldbach’s Conjecture, All primes between .. and .. are in the group .. of units in semigroup . of multiplication mod ... Due to its squarefree modulus . is a disjoint union of 2. groups, with as many idempotents—one per divisor of .., which form a Boolean lattice .. The . properties of . and its lattice are studied. It