What Is the Relationship Between m, n, and x in the 3x+1 Problem?

[FromRussiaWithLove]

working on Kollatz problem (3x+1 problem) I faced with enother hard problem on number theory. the problem is:
we have a number k that is:
k=m*(3^n)-1
where m is odd and m>0, n>0, m and n are integers
we can see that k is even and if we will divide k on 2^x we will make m1 number that is odd. The question is to find x if we know m and n. I'm sorry for my english, I know russian much better :)

 

[matt grime]

Are you attempting to say you want to know the power of two in the prime decomposition of m3^n - 1, when m is odd and n arbitrary (but integers, obviously)?

 

[FromRussiaWithLove]

yes, if it is possible. working on that problem I found in what situation the power of two is one, but it is inly a part of answer. The table of power of two for different m and n is very interesting:
n 1 2 3 4 5
m
1 1 3 1 4 1<-- the power of 2 for different m and n
3 3 1 4 1 3
5 1 2 1 2 1
7 2 1 2 1 6