A methodology of Using the Decomposition of Odd Pairs in Relation to Goldbach's Conjecture

The conjecture was first announced by Goldbach in 1742, said that every even integer greater than 2 is equal to the sum of two prime numbers. \cite{goldbach} Mathematicians have tried different methods, from analytics to computational. However, a full proof of this problem has not yet been reached until now. In this paper, we build a simple and easy to understand framework which is based on basic knowledge of number theory and the pigeonhole principle. Within 3 pages, it does not take long for the reviewer to read and comprehend our logic. Our aim is not to offer a full proof of the conjecture but a suggestion of exploring elementary methods for the traditional problems. This manuscript is shared as a preprint. Constructive mathematical feedback and suggestions for improvement are welcome and may be sent to the author via email [email protected]