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 veri?ed to be true for all even integers upto 4.1018. In this article, we prove that the conjectureis true for all integers, with at least three di?erent ways. In short, thistreaty has as objective show the proof of GC, and presents a new resolution tothe conjecture. Knowing that, these in?nities establish other groups ofin?nities, in a logical way the conviction for the method and idea of provingit, we stand and separate these groups to prove, not only a sequence, but thewhole embodiment of arithmetic properties called here as groups, as well as itsin?nity conjectured for centuries.

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