The Collatz conjecture is the simplest open problem in mathematics. You can explain it to all your non-mathematical friends, and even to small children who have just learned to divide by 2.

Dec 18, 2025 · Q&A for people studying math at any level and professionals in related fields

Aug 26, 2022 · Therefore the Collatz Conjecture is true. Every number will inevitably transform down to $1$. Sorry for the difficult to read LaTeX, kind of a new user, but feel free to criticize …

Mar 31, 2018 · For all those infinite sequences the Collatz-conjecture is immediately proven - the Collatz-transformation (in its Syracuse-formulation) goes in reverse direction of the arrows, for …

Jan 24, 2022 · The Collatz conjecture has moreover a property that most conjectures like Goldbach or Riemann do not have. If there is a diverging trajectory , we might not be able to …

Sep 25, 2015 · which extends the collatz function to the complex plane. I think the point to remember is that the way the Collatz function is written definitely influences how it's studied. …

Nov 14, 2021 · I think it makes sense to consider every case of the generalized version of the Collatz-conjecture to be a Collatz-like problem. Note that this generalized version was proven to …

Jun 28, 2021 · An analogue to the Collatz conjecture with these rules fails, because $\ 5\to 14\to 7\to 20\to 10\to\ 5\ $ is a cycle that does not contain $\ 1.\ $ In fact, there are lots of cycles …

The conjecture is that for all n ∈N n ∈ N, n n eventually converges under iteration by f f to 1 1. I was wondering if the "5n+1" problem has been solved. This problem is the same as the Collatz …

Nov 3, 2024 · Here is a curiosity about negative Collatz sequences that it would be interesting to investigate: Do the -5 loop numbers ever become more frequent than the -1 loop and -17 loop …