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On the flint hills series
Theophilus Agama
In this note, we study the flint hills 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 ess…
On addition chains and progress on the Scholz conjecture
Theophilus Agama
In this paper, we develop some new classes of methods to study the Scholz conjecture on addition chains. It turns out that the exponents of numbers of the form largely dete…
A new proof of some matrix inequalities
Theophilus Agama
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_{…
On the general no-three-in-line problem
Theophilus Agama
In this paper, we show that the number of points that can be placed in the grid for all with so that no…
On the Gap sequence and the Gilbreath conjecture
Theophilus Agama
Motivated by the Gilbreath 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 ind…
Simple close curve magnetization and application to Bellman's lost in the forest problem
Theophilus Agama
In this paper, we introduce and develop the notion of simple closed-curve magnetization. We provide an application to the Bellman lost in the forest problem by assuming special geo…