The Collatz conjecture means that for any positive integer, halve if it is even, three times plus one if it is odd, and repeat the above transformation and will eventually get one. Written in mathematical form, that for any positive integer n, there exists k such that f^k(n)=1, where f(n) is n/2 for n is even and 3n+1 for n is odd, f^k(n) refers to k iterations of f(n).

Collatz Conjecture Extension, where 3n+1 is replaced by an+b, where a is a non-zero integer, b is an integer, and n/2 is replaced by n/c, where c is a non-zero integer.

The correctness of the Collatz conjecture or extension is usually verified by verifying multiple positive integers in turn, but in this article we examine it in a different way.

To be continued