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A part of Kollatz problem

  1. Nov 15, 2004 #1
    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:
    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 :)
  2. jcsd
  3. Nov 16, 2004 #2

    matt grime

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    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)?
  4. Nov 16, 2004 #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
    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
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