Throughout history, humanity has been driven by an innate curiosity to explore beyond
established boundaries, particularly evident in scientific and mathematical pursuits. The …

The Collatz conjecture, also known as the 3x+ 1 conjecture, can be stated in terms of the
reduced Collatz function R (x)=(3x+ 1)/2h (where 2h is the larger power of 2 that divides 3x+ …

Image encryption methods aim to protect content privacy. Typically, they encompass
scrambling and diffusion. Every pixel of the image is permuted (scrambling) and its value is …

Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians
and computer scientists alike due to its simple proposal, yet intractable proof. In this paper …

Cryptocurrencies such as Bitcoin rely on a proof-of-work system to validate transactions and
prevent attacks or double-spending. A new proof-of-work is introduced which seems to be …

This study explored whether computer-assisted, project-based learning instruction can help
a twice-exceptional (2e) student increase classroom concentration, mathematical concepts …

In this chapter, the possibility of experiments in mathematics is examined. A general scheme
is proposed as a tool to handle the different forms of experiments that are being used in …

Newly discovered fundamental theories (metamathematics) of integer numbers may be used
to formalise and formulate a new theoretical number system from which other formal …

We explore aspects of an experimental approach to mathematical proof, most notably
number crunching, or the verification of subsequent particular cases of universal …

Abstract The 3x+ 1 Problem, or the Collatz Conjecture, was originally developed in the early
1930's. It has remained unsolved for over eighty years. Throughout its history, traditional …