topologies on and arithmetic applications

A NEW REPRESENTATION OF INTEGERS AND SOME RESULTS ON PRIME CONJECTURES

SOME CONGRUENCES FOR SCHR ¨ODER TYPE POLYNOMIALS

Irreducibility of truncations of the Catalan generating function

We prove that, for every positive integer $n$, the polynomial $C_0+C_1x+\cdots+C_nx^n$ is irreducible over $\mathbb{Q}$, where $C_k$ denotes the $k$th Catalan number.

Theory & Applications of Graphs Theory

Arithmetic properties of solubilizers

Let $G$ be a finite group and $x \in G$. In 2013, Hai-Reuven proved that the cardinality of the centralizer of $x$ divides the cardinality of the solubilizer of $x$. Settling a conjecture of Mousavi, Poozesh and Zamani, we show that the cardinality of the normalizer of $\langle x \rangle$ is also a divisor. We actually...

On a New Aspect of Karatsuba’s Phenomenon