Browsing by Author "Agama, Theophilus"
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Item A progress on the binary Goldbach conjecture(2022-06-08) Agama, TheophilusIn this paper, we develop the method of circle of partitions and associated statistics. As an application, we prove conditionally the binary Goldbach conjecture. We develop series of steps to prove the binary Gold-bach conjecture in full. We end the paper by proving the binary Goldbach conjecture for all even numbers exploiting the strategies outlined.Item An improved bound for length of addition chains producing $2^n-1$(2022-07-19) Agama, TheophilusIn this paper we prove that there exists an addition chain producing... #find full abstract in the attached documentItem An upper bound for the Erd\H{o}s unit distance problem in the plane(2023-02-09) Agama, TheophilusIn this paper, using the method of compression, we prove a stronger upper bound for the Erd\H{o}s unit distance problem in the plane... #find the complete abstract in the attached fileItem Complex Circles of Partition and the Asymptotic Lemoine Conjecture : Asymptotic Lemoine Conjecture(2022-10-13) Agama, Theophilus; Gensel, BerndtUsing the methods of the complex circles of partition (cCoPs), we study interior and exterior points of such structures in the complex plane. With simitarities to quotient groups inside of the group theory we define quo-tient cCoPs. With it we can prove an asymptotic version of the Lemoine Conjecture.Item Multivariate circle of partitions and the squeeze principle : Multivariate circle of partitions(2023-12-30) Agama, TheophilusThe goal of this paper is to extend the squeeze principle to circle of partitions with at least two resident points on their axes.Item On a conjecture of Erd\H{o}s on additive basis of large orders : On a conjecture of Erd\H{o}s(2022-11-08) Agama, TheophilusUsing the methods of multivariate circles of partition, we prove that for any additive base A of order h ≥ 2 the upper bound. #Check uploaded file for detailed abstractItem On The Distribution Of Perfect Numbers And Related Sequences Via The Notion Of The Disc(2022-11-21) Agama, TheophilusIn this paper we investigate some properties of perfect numbers and associated sequences using the notion of the disc induced by the sum-of-the-divisor function $\sigma$. We reveal an important relationship between perfect numbers and abundant numbers.Item On the general Erd\H{o}s-Moser equation via the notion of olloids(2022-08-23) Agama, TheophilusWe introduce and develop the notion of the olloid. We apply this notion to study a variant and a generalized version of the Erd ̋os-Moser equation under some special local condition.Item On the method of surgery and applications : surgery(2022-05-28) Agama, TheophilusIn this paper we introduce the concept of surgery. This concept ensures that almost all discontinuous functions can be made to be continuous without redefining their support. In spite of this, it preserves the properties of the original function. Consequently we are able to get a handle on the number of points of discontinuities on a finite interval by having an information on the norm of the repaired function and vice-versa.Item On the number of points included in a plane figure with large pairwise distances : On the number of points included in a plane figure(2022-06-21) Agama, TheophilusUsing the method of compression we show that the number of points that can be placed in a plane figure with mutual distances at least d > 0 satisfies the lower bound... #find the complete abstract in the attached fileItem The theory of the Collatz process and the method of dynamical balls : The theory of the Collatz process(2022-06-03) Agama, TheophilusIn this paper we introduce and develop the theory of the Collatz process and the method of dynamical balls. We leverage this theory to study the Collatz conjecture. This theory also has a subtle connection with the infamous problem of the distribution of Sophie germain primes. We also provide several formulation of the Collatz conjecture in this language. Furthermore, we introduce and develop the notion of dynamical systems induced by a fixed a ∈ N and their associated induced dynamical balls. We develop tools to study problems requiring to determine the convergence of certain sequences generated by iterating on a fixed integer.