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arXiv · 2012.01329

Studies in Additive Number Theory by Circles of Partition

Theophilus Agama·Berndt Gensel
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Abstract

In this paper, we introduce and develop the circle embedding method. This method hinges essentially on a combinatorial-geometric structure which we choose to call circles of partition. We provide applications in the context of problems that relates to deciding on the feasibility of partitioning numbers into certain subset 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 strictly greater than $\frac{1}{2}$. This possibility could herald an unprecedented progress on categories of problems of similar flavour. The paper finishes by presenting an asymptotic proof of the binary Goldbach and Lemoine conjecture as an application of the developed method.

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Theophilus Agama, Berndt Gensel. 2026-04-19. Studies in Additive Number Theory by Circles of Partition. https://arxiv.org/abs/2012.01329

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