Research Article
Exploring the influence of prime factors on collatz conjecture behavior for odd numbers: new insights and directions
Author(s): Esmaeil Farshi*
The Collatz Conjecture remains an unsolved problem in number theory, which posits that iteratively applying a simple function to any starting odd number will eventually lead to the number 1. In this paper, we investigate the behavior of the Collatz function for odd numbers with different prime factorizations using a combination of number theory, algebraic properties, and computational techniques. Our study reveals new insights into the role of prime factors and topological properties in the behavior of the Collatz function. We define the subspace H3, consisting of numbers divisible by 3, and analyze its topological properties, finding that its fundamental group is non-trivial. This suggests non-trivial behavior in the Collatz sequences for numbers in H3. We observe an intersection between the Collatz sequences for odd numbers and numbers in H3, indicating that the sequences for o.. Read More»
DOI:
10.37532/2752-8081.23.7(2).177-182
+447723598358
