## About

240

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Introduction

Theophilus Agama, an alumnus of African Institute for Mathematical Sciences Ghana, is a mathematical inventor and a problem solver. He focuses primarily on the theoretical aspect of mathematics mostly inspired by real world experience. He currently has interest in Number Theory and its allied areas, including algebra, analysis, combinatorics and geometry. Theophilus is also an ardent theory builder with very outlandish mathematical ideas drawn from intuition.

Additional affiliations

August 2017 - December 2020

Position

- Research Associate

Description

- A very versatile Mathematical Innovator who bridges almost all boundaries of various areas of mathematics, not least of which are number theory, combinatorics, discrete and Euclidean geometry , algebra, topology and classical analysis. As a problem solver, he is always on the lookout for new techniques that are outside the domain of the mathematics toolbox.

August 2014 - July 2015

Education

August 2016 - June 2017

## Publications

Publications (240)

Note: Please see pdf for full abstract with equations.
In this paper, using the method of compression, we recover the lower bound for the Erdős unit distance problem and provide an alternative proof to the distinct distance conjecture. In particular, we show that for sets of points 𝔼 ⊂ Rk concentrated around the origin with #𝔼 ∩ Nk = n/2, we have
#...

In this paper, we study the topology of problems and their solution spaces developed introduced in our first paper [1]. We introduce and study the notion of separability and quotient problem and solution spaces. This notions will form a basic underpinning for further studies on this topic.

In this paper, we study the topology ofproblems and their solution spaces developed introduced in our first paper \cite{agama2022theory}. We introduce and study the notion of separability and quotient problem and solution spaces. This notions will form a basic underpinning for further studies on this topic.

We apply the notion of the \textbf{olloid} to show that the Erd\H{o}s-Straus equation $$\frac{4}{n^{2^l}}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$$ has solutions for all $l\geq 1$ provided the equation $$\frac{4}{n}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$$ has solution for a fixed $n>4$.

Using the method of compression, we prove an inequality related to the Gauss circle problem. Let $\mathcal{N}_r$ denotes the number of integral points in a circle of radius $r>0$, then we have $$2r^2\bigg(1+\frac{1}{4}\sum \limits_{1\leq k\leq \lfloor \frac{\log r}{\log 2}\rfloor}\frac{1}{2^{2k-2}}\bigg)+O(\frac{r}{\log r}) \leq \mathcal{N}_r \leq...

Applying the pothole method on the factors of numbers of the form 2 n − 1, we prove the inequality ι(2 n − 1) ≤ n − 1 + ι(n) where ι(n) denotes the length of the shortest addition chain producing n.

Applying the pothole method on the factors of numbers of the form $2^n-1$, we prove the inequality $$\iota(2^n-1)\leq \frac{3}{2}n-\left \lfloor \frac{n-2}{2^{\lfloor \frac{\log n}{\log 2}-1\rfloor+1}}\right \rfloor-\lfloor \frac{\log n}{\log 2}-1\rfloor +\frac{1}{4}(1-(-1)^n)+\iota(n)$$ where $\lfloor \cdot \rfloor$ denotes the floor function and...

In this paper, we prove some new inequalities. To facilitate this proof, we introduce the notion of the local product on a sheet and associated space. We apply this notion to prove the main result in this paper.

In this paper we use the former of the authors developed theory of \textbf{circles of partition} to investigate possibilities to prove the binary Goldbach as well as the Lemoine conjecture. We state the \textit{squeeze principle} and its consequences if the set of all odd prime numbers is the base set. With this tool we can prove asymptotic version...

We introduce and develop the logic of existence of solution to problems. We use this theory to answer the question of Florentin Smarandache in logic. We answer this question in the negative.

We introduce and develop the logic of existence of solution to problems. We use this theory to answer the question of Florentin Smarandache in logic. We answer this question in the negative.

In this paper we use the former of the authors developed theory of circles of partition to investigate possibilities to prove the binary Goldbach as well as the Lemoine conjecture. We state the squeeze principle and its consequences if the set of all odd prime numbers is the base set. With this tool we can prove asymptotic versions of the binary Go...

Using the methods of multivariate circles of partition, we prove that for any additive base $\mathbb{A}$ of order $h\geq 2$ the upper bound $$\# \left \{(x_1,x_2,\ldots,x_h)\in \mathbb{A}^h~|~\sum \limits_{i=1}^{h}x_i=k\right \}\ll_{h}\log k$$ holds for sufficiently large values of $k$ provided the counting function $$\# \left \{(x_1,x_2,\ldots,x_h...

Using the methods of multivariate circles of partition, we prove that for any additive base $\mathbb{A}$ of order $h\geq 2$ the upper bound $$\# \left \{(x_1,x_2,\ldots,x_h)\in \mathbb{A}^h~|~\sum \limits_{i=1}^{h}x_i=k\right \}\ll_{h}\log k$$ holds for sufficiently large values of $k$ provided the counting function $$\# \left \{(x_1,x_2,\ldots,x_h...

In 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 σ. We reveal an important relationship between perfect numbers and abundant numbers.

Using the methods of the complex circles of partition (cCoPs), we study interior and exterior points of such structures in the complex plane. With similarities to quotient groups inside of the group theory we define quotient cCoPs. With it we can prove an asymptotic version of the Lemoine Conjecture.

In this work, we continue the complex circle of partition development that was started in our foundational study [3]. With regard to a cCoP and its embedding circle, we define interior and exterior points. On this foundation , we expand the concept of point density, established in [2], to include complex circles of partition. We propose the idea of...

In this work, we continue the complex circle of partition development that was started in our foundational study [3]. With regard to commandits embedding circle, we define interior and exterior points. On this foundation, we expand the concept of point density, established in [2], to include complex circles of partition. We propose the idea of a qu...

We apply the notion of the olloid to show that a certain set contains no solution of the Erdős-Straus equation.

In this note we prove a multivariate analogue of Jensen's inequality via the notion of the local product and associated space.

We introduce and develop the notion of theolloid.
We applythis notion to study a variant and a generalized version of the Erd ̋os-Moserequation under some special local condition.

We introduce and develop the notion of the olloid. We apply this notion to study the Erdős-Moser equation.

In this paper we continue the development of the circles of partition by introducing the notion of complex circles of partition. This is an enhancement of such structures from subsets of the natural numbers as base sets to the complex area as base and bearing set. Here only basics are demonstrated. This paper forms the basis for more detailed paper...

In this paper we show that the shortest length $\iota(n)$ of addition chains producing numbers of the form $2^n-1$ satisfies the lower bound $$\iota(2^n-1)\geq n+\lfloor \frac{\log (n-1)}{\log 2}\rfloor$$
where $\lfloor \cdot \rfloor$ denotes the floor function.

In this paper we show that the shortest length (n) of addition chains producing numbers of the form 2n−1 satisfies the lower boundι(2n−1)≥n+blog(n−1)log 2cwhereb·cdenotes the floor function

In this paper we prove that there exists an addition chain producing $2^n-1$ of length $\delta(2^n-1)$ satisfying the inequality
\begin{align}
\delta(2^n-1)\leq 2n-1-\left \lfloor \frac{n-1}{2^{\lfloor \frac{\log n}{\log 2}\rfloor}}\right \rfloor-\lfloor \frac{\log n}{\log 2}\rfloor +\iota(n)\nonumber
\end{align}where $\lfloor \cdot \rfloor$ denote...

In this paper we prove that there exists an addition chain producing $2^n-1$ of length $\delta(2^n-1)$ satisfying the inequality
\begin{align}
\delta(2^n-1)\leq 2n-1-2\left \lfloor \frac{n-1}{2^{\lfloor \frac{\log n}{\log 2}\rfloor}}\right \rfloor+\lfloor \frac{\log n}{\log 2}\rfloor\nonumber
\end{align}where $\lfloor \cdot \rfloor$ denotes the flo...

In this paper we study the global electrostatic energy behaviour of mutually repelling charged electrons on the surface of a unit-radius sphere. Using the method of compression, we show that the total electrostatic energy $U_k(N)$ of $N$ mutually repelling particles on a sphere of unit radius in $\mathbb{R}^k$ satisfies the lower bound
\begin{align...

In this note, we prove the inequality
\begin{align}
\bigg| \int \limits_{|a_n|}^{|b_n|} \int \limits_{|a_{n-1}|}^{|b_{n-1}|}\cdots \int \limits_{|a_1|}^{|b_1|}\cos \bigg(\frac{\sqrt[4s]{\sum \limits_{j=1}^{n}x^{4s}_j}}{||\vec{a}||^{4s+1}+||\vec{b}||^{4s+1}}\bigg)dx_1dx_2\cdots dx_n\bigg| \leq \frac{\bigg|\prod_{i=1}^{n}|b_i|-|a_i|\bigg|}{|\Re(\lan...

In this paper we prove an inequality relating the length of addition chains producing number of the form $2^n-1$ to the length of their shortest addition chain producing their exponents. In particular, we obtain the inequality $$\delta(2^n-1)\leq n-1+\iota(n)+G(n)$$ where $\delta(n)$ and $\iota(n)$ denotes the length of an addition chain and the sh...

Using 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
\begin{align}
\gg_2 d^{d-1+\epsilon}\nonumber
\end{align}for some small $\epsilon>0$.

In this note we, we prove the inequality
\begin{align}
\int \limits_{|a_n|}^{|b_n|} \int \limits_{|a_{n-1}|}^{|b_{n-1}|}\cdots \int \limits_{|a_1|}^{|b_1|}\frac{1}{\sqrt[4s+3]{\sum \limits_{j=1}^{n}x^{4s+3}_j}}dx_1dx_2\cdots dx_n \geq \frac{2\pi \times |\log (\langle a,b \rangle)|\bigg|\prod_{j=1}^{n}|b_j|-|a_j|\bigg|}{||\vec{a}||^{4s+4}+||\vec{b}...

In this note we introduce the notion of the local product on a sheet and associated space. As an application, we prove that for $\langle a,b \rangle>e^e$ then
\begin{align}
\int \limits_{|a_n|}^{|b_n|} \int \limits_{|a_{n-1}|}^{|b_{n-1}|}\cdots \int \limits_{|a_1|}^{|b_1|}\bigg|\log \bigg(i\frac{\sqrt[4s]{\sum \limits_{j=1}^{n}x^{4s}_j}}{||\vec{a}|...

In this note, we introduce the notion of the local product on a sheet and associated space. As an application, we prove that some inequalities of multiple integrals of the distance and the log normalized distance of vectors in space.

In 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 outli...

In this paper we prove that there infinitely many cousin primes by deducing the lower bound
\begin{align}
\sum \limits_{\substack{p\leq x\\p,p+4\in \mathbb{P}\setminus \{2\}}}1\geq (1+o(1))\frac{x}{2\mathcal{C}\log^2 x}\nonumber
\end{align}where $\mathcal{C}:=\mathcal{C}(4)>0$ fixed and $\mathbb{P}$ is the set of all prime numbers. In particular i...

In this paper we introduce the concept of surgery. This conceptensures 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...

In this paper we introduce and develop the method of diagonal-ization of functions f : N −→ R. We apply this method to show that the equations of the form Γr(n) + k = m 2 has a finite number of solutions n ∈ N with n > r for a fixed k, r ∈ N, where Γr(n) = n(n − 1) · · · (n − r) is the r th truncated Gamma function.

Let δ(n) denotes the length of an addition chain producing n. In this paper we prove that the exists an addition chain producing 2 n − 1 whose length satisfies the inequality δ(2 n − 1) n − 1 + ι(n) + n log n + 1.3 log n n−1 2 2 dt log 3 t + ξ(n) where ξ : N −→ R. As a consequence, we obtain the inequality ι(2 n − 1) n − 1 + ι(n) + n log n + 1.3 lo...

Using the method of compression we show that the number of integral points in the annular region induced by two k dimensional spheres of radii r and R with R > r satisfies the lower bound N R,r,k (R k−1 − r k+δ) √ k. for some small δ > 0 with k > δ(log r) log R−log r .

In this paper we study a particular class of polynomials. We study the distribution of their zeros, including the zeros of their derivatives as well as the interaction between this two. We prove a weak variant of the sendov conjecture in the case the zeros are real and are of the same sign.

Using the method of compression, we show that volume V ol(K) of a ball K in R n with a single lattice point in it's interior as center of mass satisfies the lower bound V ol(K) n n √ n thereby disproving the Ehrhart volume conjecture, which claims that the upper bound must hold V ol(K) ≤ (n + 1) n n! for all convex bodies with the required property...

In this paper we extend the so-called notion of addition chains and prove an analogue of Scholz's conjecture on this chain. In particular, we obtain the inequality ι n−1 2 (2 n − 1) ≤ n + ι(n) where ι(n) and ι n−1 2 (n) denotes the length of the shortest addition chain and the shortest addition chain of degree n−1 2 , respectively, producing n.

Using the method of compression we obtain a lower bound for the average number of d r-unit distances that can be formed from a set of n points in the euclidean space R k. By letting D n,d r denotes the number of d r-unit distances (r > 1 fixed) that can be formed from a set of n points in R k , then we obtain the lower bound 1≤d≤t D n,d r n 2r √ k...

See manuscript PDF for complete Abstract
In this paper we introduce and develop the notion of spanning of integers along functions f : N → R. We apply this method to a class of problems requiring to determine if the equations of the form tf(n) = n-k has a solution n ∈ N for a fixed k ∈ N and some t ∈ N. In particular, we show that
where φ is the...

We provide a brief survey of the Scholz conjecture and recent progress.

Using the method of compression, we show that the number of integral points on the boundary of a k-dimensional sphere of radius r satisfies the lower bound N r,k r k−1 √ k.

In this paper we study a particular class of polynomials. We study the distribution of their zeros, including the zeros of their derivatives as well as the interaction between this two. We prove a weak variant of the sendov conjecture in the case the zeros are real and are of the same sign.

Using the method of compression we obtain a generalized lower bound for the number of d-unit distances that can be formed from a set of n points in the euclidean space R k. By letting D n,d denotes the number of d-unit distances that can be formed from a set of n points in R k , then we obtain the lower bound D n,d n √ k d .

In this paper we introduce and develop the notion of spanning of integers along functions f : N −→ R. We apply this method to a class of problems requiring to determine if the equations of the form tf (n) = n − k has a solution n ∈ N for a fixed k ∈ N and some t ∈ N. In particular, we show that #{n ≤ s | tϕ(n) + 1 = n, t, n ∈ N} ≥ s 2 log s p|s (1...

In this article we study the influence of access to information among UHAS students concerning the clarion call to be pro-environmental on their resolution to be attitudinally pro-environmental. We first examined the influence of gender and study level of UHAS students on their natural inclination to be pro-environmental, where there appears to be...

In this paper we prove an inequality relating the length of addition chains producing number of the form 2 n − 1 to the length of their shortest addition chain producing their exponents. In particular, we obtain the inequality δ(2 n − 1) ≤ n − 1 + ι(n) + G(n) where δ(n) and ι(n) denotes the length of an addition chain and the shortest addition chai...

We provide an expert advice to early career researchers on manuscript preparation.

We obtain a partial solution to the Bellman lost in the forest problem using an algorithmic based approach based on close curve magnetization.

In this paper, we study the notion of dominating number of expansions .

In this paper, we study the notion of an index of sub-expansions in an expansion. We prove the index inequality as an application.

In this paper, we continue the development of multivariate expansivity theory. We introduce and study the notion of an exact expansion and exploit some applications.

Using the method of compression we show that the number of integral points in the region bounded by the $2r\times 2r \times \cdots \times 2r~(k~times)$ grid containing the sphere of radius $r$ and a sphere of radius $r$ satisfies the lower bound
\begin{align}
\mathcal{N}_{r,k} \gg r^{k-\delta}\times \frac{1}{\sqrt{k}}\nonumber
\end{align}for some s...

Using the method of compression we show that the number of integral points in a $k$ dimensional sphere of radius $r>0$ is
\begin{align}
N_k(r)\gg \sqrt{k} \times r^{k-1+o(1)}.\nonumber
\end{align}

Using the method of compression we show that the number of integral points in the region bounded by the $2r\times 2r$ grid containing the circle of radius $r$ and a circle of radius $r$ satisfies the lower bound
\begin{align}
\mathcal{N}_r \gg r^{2-\delta}\nonumber
\end{align}for some small $\delta>0$.

In this note we introduce the notion of the local product on a sheet and associated space. As an application we prove under some special conditions the following inequalities
\begin{align}
2\pi \frac{|\log(\langle \vec{a},\vec{b}\rangle)|}{(||\vec{a}||^{4s+4}+||\vec{b}||^{4s+4})|\langle \vec{a},\vec{b}\rangle|}\bigg |\int \limits_{|a_n|}^{|b_n|} \...

In this paper we continue with the development of the circles of partitions by introducing the notion of the area induced by circles of partitions and explore some applications.

In this paper we introduce and develop the method of diagonal-ization of functions f : N −→ R. We apply this method to a class of problems requiring to determine if the equations of the form f (n) + k = m 2 has a finite number of solutions n ∈ N for a fixed k ∈ N.

In this paper we introduce a multivariate version of circles of partition introduced and studied in [1]. As an application we prove a weaker general version of the Erdős-Turán additive base conjecture. The actual Erdős-Turán additive base conjecture follows from this general version as a consequence.

In this paper we use a new method to study problems in additive number theory. We leverage this method to prove the Lemoine conjecture, a closely related problem to the binary Goldbach conjecture. In particular, we show by using the notion of circles of partition that for all odd numbers n ≥ 9 holds n = p + 2q for not necessarily different primes p...

In this paper we prove the binary Goldbach conjecture. By exploiting the language of circles of partition, we show that for all sufficiently large n ∈ 2N # {p + q = n| p, q ∈ P} > 0. This proves that every sufficiently large even number can be written as the sum of two prime numbers.

In this paper we study an extension of the Euler totient function to the rationals and explore some applications. In particular, we show that
\begin{align}
\# \{\frac{m}{n}\leq \frac{a}{b}~|~m\leq a,~n\leq b,~\gcd(m,a)=\gcd(n,b)=1,~\gcd(n,a)>1\nonumber \\~\vee~\gcd(m,b)>1~\vee ~\gcd(m,n)>1\}=\sum \limits_{\substack{\frac{m}{n}\leq \frac{a}{b}\\mn\...

In this paper we prove Lemoine's conjecture. By exploiting the language of circles of partition, we show that for all sufficiently large n ∈ 2N+1 # {p + 2q = n| p, q ∈ P} > 0. This proves that every sufficiently large odd number can be written as the sum of a prime and a double of a prime.

In this note we introduce the notion of the outer product of elements in a vector space. We study their properties and explore their applications. In particular, we show that under certain conditions the inequality holds ∑ λ i ∈Spec(ab T) min{log |t − λ i |} [||a||,||b||] #Spec(ab T) log ||b|| + ||a|| 2 + 1 ||b|| − ||a|| ∑ λ i ∈Spec(ab T) log 1 − 2...

In this note, we introduce the notion of the disc induced by an arithmetic function and apply this notion to the odd perfect number problem. We show that no odd perfect numbers exist by exploiting this concept.

In this paper we introduce and develop the notion of simple close curve magnetization. We provide an application to Bellman’s lost in the forest problem assuming special geometric conditions between the hiker and the boundary of the forest.

We introduce and study the needle \begin{align}(\Gamma_{\vec{a}_1} \circ \mathbb{V}_m)\circ \cdots \circ (\Gamma_{\vec{a}_{\frac{l}{2}}}\circ \mathbb{V}_m):\mathbb{R}^n\longrightarrow \mathbb{R}^n.\nonumber
\end{align} By exploiting the geometry of compression, we prove that this function is a function modeling an $l$-step self avoiding walk for $l...

In this paper 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.

In this note we study the flint hill series of the form \begin{align} \sum \limits_{n=1}^{\infty}\frac{1}{(\sin^2n) n^3}\nonumber \end{align}via a certain method. The method works essentially by erecting certain pillars sufficiently close to the terms in the series and evaluating the series at those spots. This allows us to relate the convergence a...

In 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 by showing that\begin{align}\# \bigg\{||\vec{x_j}-\vec{x_t}||:\vec{x}_t, \vec{x_j}\in \mathbb{E}\subset \mathbb{R}^2,~||\vec{x_j}-\vec{x_t}||=1,~1\leq t,j \leq n\bigg\}\ll_2 n^{1+o(1)}.\nonumber
\end{align}

In this paper we study the shortest addition chains of numbers of special forms. We obtain the crude inequality $$\iota(2^n-1)\leq n+1+G(n)$$ for some function $G:\mathbb{N}\longrightarrow \mathbb{N}$. In particular we obtain the weaker inequality $$\iota(2^n-1)\leq n+1+\left \lfloor \frac{n-2}{2}\right \rfloor$$ where $\iota(n)$ is the length of t...

In 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 Goldbach conjecture in full. We end the paper by proving the binary Goldbach conjecture for all even numbers exploiting the strategies outlined...

In this paper we show that the number of points that can be placed in the grid $n\times n\times \cdots \times n~(d~times)=n^d$ for all $d\in \mathbb{N}$ with $d\geq 2$ such that no three points are collinear satisfies the lower bound
\begin{align}
\gg_d n^{d-1}\sqrt[2d]{d}.\nonumber
\end{align}This pretty much extends the result of the no-three-in-...

In this paper we show that the number of points that can be placed in the grid $n\times n\times \cdots \times n~(d~times)=n^d$ for all $d\in \mathbb{N}$ with $d\geq 2$ such that no three points are collinear satisfies the lower bound \begin{align} \gg n^{d-1}\sqrt{d}\mathrm{min}_{\vec{x}\in n^d}\mathrm{Inf}(x_j)_{j=1}^{d}.\nonumber \end{align}This...

Let $\mathcal{R}\subset \mathbb{R}^n$ be an infinite set of collinear points and $\mathcal{S}\subset \mathcal{R}$ be an arbitrary and finite set with $\mathcal{S}\subset \mathbb{N}^n$. Then the number of points in $\mathcal{S}$ with mutual integer distance satisfies the lower bound
\begin{align}
\gg |\mathcal{S}|\sqrt{n}\mathrm{min}_{\vec{x}\in \ma...

In this paper we formulate and prove several variants of the Erdös-Turán additive bases conjecture.

In this paper we show under some special conditions that the natural density of Ulam numbers is zero.

In this paper we study the convergence of the flint hill series of the form
\begin{align}
\sum \limits_{n=1}^{\infty}\frac{1}{(\sin^2n) n^3}\nonumber
\end{align}via a certain method. The method works essentially by erecting certain pillars sufficiently close to the terms in the series and evaluating the series at those spots. This allows us to rela...

In this paper we give alternate proofs of some well-known matrix inequalities. In particular, we show that under certain conditions the inequality holds \begin{align}\sum \limits_{\lambda_i\in \mathrm{Spec}(ab^{T})}\mathrm{min}\{\log |t-\lambda_i|\}_{[||a||,||b||]}&\leq \# \mathrm{Spec}(ab^T)\log\bigg(\frac{||b||+||a||}{2}\bigg)\nonumber \\&+\frac{...

In this paper we introduce and study the notion of singularity, the kernel and analytic expansions. We provide an application to the existence of singularities of solutions to certain polynomial equations.

In this paper we introduce and develop a method for studying problems concerning packing and covering dilemmas and explore some potential applications.

Motivated by Gilbreath's conjecture, we develop the notion of the gap sequence induced by any sequence of numbers. We introduce the notion of the path and associated circuits induced by an originator and study the conjecture via the notion of the trace and length of a path.

## Questions

Question (1)

Should self acclaimed experts - only in tune with protracted self accumulated knowledge within their field and usually crossed with new ideas - be at the forefront and trusted in validating a scientific contribution? Would there ever be an age where AI will solely validate the authenticity of a manuscript encapsulating a scientific finding? This appears to not be a far distant prospect but questions lingers on the time scale.

## Projects

Projects (25)

We introduce and develop the logic of existence of solution to problems. We use this theory to answer the question of Florentin Smarandache in logic. We answer this question in the negative.

We introduce and develop the concept of the planar measure of matrices. This notion is a generalization of the notion of the trace in matrix theory.

We develop the method of spanning a set of integers along a function. We apply this method to study the Lehmer totient problem.