Studies in Additive Number Theory by Circles of Partition

2020/12/02 by Agama, Theophilus, Gensel, Berndt
#11H99 #FOS: Mathematics #General Mathematics (math.GM) #Primary 11P32 11A41 #Secondary 11B13

paper · doi:10.48550/arxiv.2012.01329

Abstract

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∈ℕ into any set ℍ with natural density greater than (1)/(2). This possibility could herald an unprecedented progress on class of problems of similar flavour. The paper finishes by giving an asymptotic proof of the binary Goldbach and the Lemoine conjecture as application of the developed method..

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