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An Algebraic Approach to the Goldbach Conjecture
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Abstract: This paper will give both the necessary and sufficient conditions required to
find a counter-example to the Goldbach Conjecture by using an algebraic
approach where no knowledge of the gaps between prime numbers is needed. It
will then be shown that it is impossible for such a counter-example to exist.
To begin, let $2a$ be a counter-example to the Goldbach Conjecture where $a \in
\mathbb{N}$, non-prime, and $a > 3$. It will be shown using the closure
property of the integers, along with the Fundamental ...
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