Journal of Modern Technology and Engineering

The Collatz Conjecture goes beyond being merely a subject of mathematical and scientific study. From the perspective of Computer Engineering and Computer Science, not only does it serve as an important collaborative area in such scientific research, but the conjecture algorithm is also utilized in various practical application domains. These applications of the Collatz Conjecture offer innovative solutions, particularly in fields such as data security, encryption, and digital authentication. Recent studies on the mathematical foundation and application areas of the conjecture provide new perspectives on both the mathematical resolution of the problem and its potential technological uses. In this study, some mathematical expressions derived from the Collatz Procedure are presented, and a method is proposed to determine these expressions algorithmically. The proposed algorithm has been demonstrated through examples. These expressions and the algorithm may prove useful in both the proof and practical applications of the Collatz Conjecture.