**Conjecture**Let if is odd and if is even. Let . Assume we start with some number and repeatedly take the of the current number. Prove that no matter what the initial number is we eventually reach .

This problem is also called Collatz conjecture, Ulam conjecture, or the Syracuse problem. For a more extensive discussion, visit the wikipedia article or [L].

## Bibliography

[L] Jeffrey C. Lagarias: The 3x+1 problem: An annotated bibliography (1963--2000)

* indicates original appearance(s) of problem.