How to write a pseudocode program that halts only if the Collatz Conjecture is false.
Thanks much in advance!!!
If the Collatz-conjecture is false, then we have either a "nontrivial" cycle (we have some in the domain of negative integers) or a divergent trajectory.
If we check all numbers, whether their trajectory arrives at 1 and find, that on a certain trajectory an earlier number occurs a second time, then the program may halt and print "collatz conjecture false for integer [n]" where [n] is the first number which signalled the occurence of a cycle.
However, this does not detect (and then halt the program) if we arrive at a divergent trajectory - so this answers your question only half way...