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 veriï¬ed 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 diï¬erent ways. In short, this treaty has asobjective show the proof of GC, and presents a new resolution to the conjecture.Knowing that, these inï¬nities establish other groups of inï¬nities, 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 inï¬nity conjecturedfor centuries.

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