Number Theory

    

The Circle Embedding Method and Applications

Authors: Theophilus Agama, Berndt Gensel

In this paper we introduce and develop the circle embedding method. This method hinges essentially on a Combinatorial structure which we choose to call circles of partition. We provide applications in the context of problems relating to deciding on the feasibility of partitioning numbers into certain class of integers. In particular, our method allows us to partition any sufficiently large number $n\in\mathbb{N}$ into any set $\mathbb{H}$ with natural density greater than $\frac{1}{2}$. This possibility could herald an unprecedented progress on class of problems of similar flavour. The paper finishes by giving a partial proof of the binary Goldbach conjecture.

Comments: 48 Pages. A partial proof of the Goldbach conjecture added.

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Submission history

[v1] 2020-09-24 12:11:29
[v2] 2020-11-04 20:15:15
[v3] 2020-11-30 08:49:40
[v4] 2021-01-29 04:32:47

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