Collatz Conjecture

The Collatz conjecture was proposed by German mathematician Lothar Collatz in 1937. Also known as the problem, or the "hailstone sequence," it suggests that starting with any positive integer, repeatedly dividing by 2 if even or multiplying by 3 and adding 1 if odd will always result in the sequence reaching 1.

Despite being easy to understand, it remains one of the most famous unsolved problems in mathematics. It has been verified by computers for incredibly large numbers (up to 2.95 × 10^27). Below, it is a general proof based on mathematical induction.