The Strong Goldbach conjecture, GC, dates backto 1742. It states that every even integer greater than four can be written asthe sum of two prime numbers. Since then, no one has been able to prove theconjecture. The conjecture has been veriﬁed to be true for all even integers upto 4.1018. In this article, we prove that the conjecture is true for allintegers, with at least three diﬀerent ways. In short, this treaty has asobjective show the proof of GC, and presents a new resolution to the conjecture.Knowing that, these inﬁnities establish other groups of inﬁnities, in a logicalway the conviction for the method and idea of proving it, we stand and separatethese groups to prove, not only a sequence, but the whole embodiment ofarithmetic properties called here as groups, as well as its inﬁnity conjecturedfor centuries.

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