Number Theory


New Abelian Groups for Primes of Type 4K-1 and 4K+1.

Authors: Anna Povazanova, Ivo Povazan

p is prime.The article describes the new Abelian groups of type p=4k+1 and p = 4k-1, for which a theorem similar to the Fermat's little theorem applies. The multiplicative group (Z/pZ)* in some sense similar to the Abelian group of type p = 4k+1. Abelian group of type p = 4k-1 is a different structure compared to group (Z/pZ)*. This fact is used for the primality test of integer N = 4k-1. The primality test was veried up to N = 2^(64).

Comments: 13 Pages.

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Submission history

[v1] 2018-10-12 02:45:55

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