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

  • Thread starter FromRussiaWithLove
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In summary, the problem at hand is to find the power of two in the prime decomposition of m3^n - 1, where m is an odd integer greater than zero and n is a positive integer. The table provided shows the power of two for different values of m and n, with the most interesting pattern being that the power of two is one when m is equal to 1 and n is odd. However, this is only a part of the answer and further exploration is needed to fully understand the problem.
  • #1
FromRussiaWithLove
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0
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 :)
 
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  • #2
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)?
 
  • #3
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
 

1. What is the Kollatz problem?

The Kollatz problem, also known as the Collatz conjecture or 3n+1 problem, is a mathematical conjecture that states that for any positive integer, if it is even, divide it by 2, and if it is odd, multiply it by 3 and add 1. This process will eventually lead to the number 1.

2. Who proposed the Kollatz problem?

The Kollatz problem was first proposed by German mathematician Lothar Collatz in 1937.

3. Has the Kollatz problem been solved?

No, the Kollatz problem has not been solved. It remains an unsolved mathematical conjecture, and it is considered one of the most notorious unsolved problems in mathematics.

4. What is the significance of the Kollatz problem?

The Kollatz problem has significant implications in various fields of mathematics, such as number theory, chaos theory, and computer science. It has also sparked interest in many areas of research, including the study of mathematical functions and the behavior of iterative algorithms.

5. Can the Kollatz problem be solved?

As of now, there is no known solution to the Kollatz problem. Many mathematicians have attempted to find a proof or disproof of the conjecture, but it remains an open problem. Some believe that it may never be solved, while others continue to search for a solution.

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