Topic of Research Seminar: The 3x+1 problem and its Generalization

Abstract: The 3n + 1 Problem, proposed by Lothar Collatz, concerns the iteration of a function that transforms positive odd integers to and even integers to The conjecture suggests that repeated iterations of the function will eventually bring any positive integer to . This seminar aims to present a probabilistic approach to determine the proportion of numbers that do not reach . Additionally, it focuses on categorizing numbers into congruence classes and demonstrates the classes that satisfy the conjecture. Furthermore, it briefly investigates the behavior of negative numbers under the function and proposes a conjecture for this scenario. The seminar will also revisit and interpret the findings of Terras from his paper, “A Stopping Time Problem on the Positive Integers,” providing a comprehensive overview and updated insights into this intriguing mathematical problem.

Subject Field of Topic: Number Theory

Name of Speaker: Imtiaz Waheed

Professorial Rank of Speaker: PhD Students (Mathematics Dpt.) SNS – NUST

Email of Speaker: [email protected]

Affiliation of Speaker: School of Natural Sciences (SNS), NUST

Date and Venue: (Wednesday) 22 May 2024, 15:30 hrs, at CR #205 (New SNS Building), School of Natural Sciences (SNS), NUST Islamabad