Congruence theory has many applications in physical, social, biological and technological
systems. Congruence arithmetic has been a fundamental tool for data security and computer …

It was long assumed that the pseudorandom distribution of prime numbers was free of
biases. Specifically, while the prime number theorem gives an asymptotic measure of the …

In this paper, we propose a network whose nodes are labeled by the composite numbers
and two nodes are connected by an undirected link if they are relatively prime to each other …

Large series of prime numbers can be superposed on a single quantum register and then
analyzed in full parallelism. The construction of this Prime state is efficient, as it hinges on …

Investigation of divisibility properties of natural numbers is one of the most important themes
in the theory of numbers. Various tools have been developed over the centuries to discover …

We show how the cross-disciplinary transfer of techniques from dynamical systems theory to
number theory can be a fruitful avenue for research. We illustrate this idea by exploring from …

The Erdős-Rényi (ER) random graph G (n, p) analytically characterizes the behaviors in
complex networks. However, attempts to fit real-world observations need more sophisticated …

In the emerging field of network science, a recent model proposes that a hyperbolic
geometry underlies the network representation of complex systems, shaping their topology …

Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of
research, many questions remain still unsolved. In recent years, computer simulations are …

This research used the standard system modeling techniques of normal vectors, Doppler
vectors, trigonometric relationships, and growth ratios to evaluate the systemic interactions …