The Collatz Conjecture, also known as the 3n+1 Conjecture, is an unsolved mathematical problem that has intrigued mathematicians for many years. Proposed by German mathematician Lothar Collatz in 1937, it is a simple iterative process that involves repeatedly applying a particular algorithm to a positive integer.
The conjecture states that for any positive integer n, the sequence obtained by repeatedly applying the following rules will eventually reach the value 1:
If n is even, divide it by 2. If n is odd, multiply it by 3 and add 1. For example, starting with the number 6, the sequence would be 6, 3, 10, 5, 16, 8, 4, 2, 1. Despite the simplicity of the rules, the Collatz Conjecture remains an open question, as no counterexamples have been found.
Mathematicians have extensively tested the conjecture using computers, and it holds for an enormous range of numbers. However, due to the exponential growth of the sequence, it becomes increasingly difficult to prove that it holds for all numbers.
The Collatz Conjecture is a fascinating problem in the field of number theory and has attracted significant attention from mathematicians worldwide. Its simplicity, coupled with its unsolved nature, makes it an intriguing puzzle that continues to captivate mathematicians and researchers to this day.
