THE COLLATZ CONJECTURE

The Collatz conjecture is a famous unsolved problem in mathematics, also known as the 3n+1 conjecture, the Ulam conjecture, or the Syracuse problem. It is a deceptively simple problem, yet it has stumped mathematicians for decades.

The conjecture involves starting with any positive integer n and performing the following steps repeatedly: 1st: If n is even, divide it by 2. 2nd: If n is odd, multiply it by 3 and add 1.

For example, starting with n=6, we get the following sequence: 6, 3, 10, 5, 16, 8, 4, 2, 1. The sequence eventually reaches 1, and then continues in the loop 1, 4, 2, 1, 4, 2, 1, and so on.

The Collatz conjecture states that no matter what positive integer n you start with, this sequence will eventually reach 1. However, despite extensive computational evidence supporting the conjecture for numbers up to 2^60, no one has been able to prove it for all numbers.

The Collatz conjecture is a problem that is easy to state, but has proved incredibly difficult to solve. It has connections to many areas of mathematics, including number theory & graph theory. No one has been able to definitively prove or disprove it.