I have thought of a single simple rule for Colatz conjecture that is slightly different to the normal one. Here it is: $$f:(a,b)\rightarrow (3a+\gcd(a,b),b)$$ Then the Colatz conjecture can be written as: $$\forall_{n:\mathbb{N}}\exists_{m:\mathbb{N}}\exists_{p:\mathbb{N}}\{ f^p(n,2^m) = (2^m,2^m...

Disclaimer: I'm not a mathematician and for the most part I do not understand what, exactly, it takes to mathematically prove anything. That is where this question comes from. Why can't the Collatz Conjecture be proven by showing that all even numbers less than 11 do "resolve" (via the collatz di...