On a class of conjectures equivalent to the strong Goldbach's conjecture

Abstract

In the paper are considered two different semigroups whose elements are positive integer-value multiplicative functions. Each element of the union of these semigroups generates an assertion that presents a conjecture equivalent (as proved in the paper) to the Strong Goldbach's Conjecture (see [1], [2]): SG: Every even number greater than or equal to 8 is a sum of two odd distinct primes. Our investigation presents a new point of view for the Goldbach's Conjecture and suggests a strong generalization of some of the results in [2] and [3]. (Remark. The classical Goldbach's Conjecture: Every even number greater than 4 is a sum of two primes is a corollary from SG.)