# All posts tagged: collatz conjecture

## A Possible Proof of Collatz Conjecture

Our reader Eswar Chellappa has sent his work on the solution of ‘3X+1′ problem, also called Collatz Conjecture. He had been working on the proof of Collatz Conjecture off and on for almost ten years. The Collatz Conjecture can be quoted as follow: Let $\phi : \mathbb{N} \to \mathbb{N}^+$ be a function defined  such that: $$\phi(x):= \begin{cases} \frac{x}{2}, & \text{if } x \text{ is even } \\ 3x+1, & \text{ if } x \text{ is odd} \end{cases}$$ Then the iterates of $\phi(x)$ will eventually reach $1$ for any initial value of $x$. See this post about Collatz Conjecture for more details.  Plenty of proof attempts were made by various mathematicians. But none of those could flawlessly prove the statement. Mr. Chellappa’s attempt is based upon the famous Sieve of Eratosthenes. Despite of his experience & confidence, I can not guarantee if this work is perfect. I invite readers to cross check the flawlessness and tell what they think.   Introduction Let, $f(x) = x/2$ if $x$ is even and  $g(x) = 3x + 1$ if $x$ is odd. …

## The Collatz Conjecture : Unsolved but Useless

The Collatz Conjecture is one of the Unsolved problems in mathematics, specially in Number Theory. The Collatz Conjecture is also termed as 3n+1 conjecture, Ulam Conjecture, Kakutani’s Problem, Thwaites Conjecture, Hasse’s Algorithm, Syracuse Problem.