thank you, very much! that's a lot of money. if i win it, i'll travel to japan to meet Yoshihiro Togashi
Best of luck this is a very hard problem. Japanese company Bakuage offers 120M JPY (around 1M dollars) for a proof per https://www.prnewswire.com/news-releases/bakuage-offers-prize-of-120-million-jpy-to-whoever-solves-collatz-conjecture-math-problem-unsolved-for-84-years-301326629.html
n is a positive integer.
a positive integer is an integer that is greater than zero.
the smallest possible positive integer is 1.
every positive integer is even or odd.
for some positive integer k:
-> n is even if can be written as 2k.
-> n is odd if can be written as 2k-1.
f(n) = {n/2 if n is even; 3n+1 if n is odd}.
=> f(n) = {n/2 if n=2k; 3n+1 if n=2k-1}, k>=1.
=> f(n) = {(2k)/2 if n=2k; 3(2k-1)+1 if n=2k-1}, k>=1.
=> f(n) = {k if n=2k; (6k-3)+1 if n=2k-1}, k>=1.
=> f(n) = {k if n=2k; 6k-2 if n=2k-1}, k>=1.
=> f(n) = {k if n=2k; 2(3k-1) if n=2k-1}, k>=1.