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Math Help - Mersenne numbers

  1. #1
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    Mersenne numbers

    Hello. I've got three questions.
    1.Can a Mersenne number be a multiple of another Mersenne number? Prove. (I mean is that possible that 2^a - 1 | 2^b - 1 where a, b are prime numbers)
    2.Can a Mersenne number be equal to X^n ? (X and n are integer). Prove. (This Mersenne number is 2^d - 1 where d is a prime number)
    3.Is it possible that (2^t - 1)^a * (2^u - 1)^b is equal to 2^tu - 1? (t, u, 2^t -1, 2^u -1 are prime numbers).
    Last edited by helgamauer; November 12th 2010 at 07:15 AM.
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  2. #2
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    1. If [LaTeX ERROR: Convert failed] " alt="p_{1}[/Math] and [LaTeX ERROR: Convert failed] " />[LaTeX ERROR: Convert failed] can be written as 2ak+1[/Math] , for some [Math]k\in\mathbb{N}. We need a trick, I think.
    Last edited by Demandeur; November 12th 2010 at 10:05 PM.
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  3. #3
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    Hint:

    1. Follows direclty from this (more generic) result
    If (m,n) = 1 then (2^m - 1, 2^n-1) = 1

    Can you prove the above result?
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  4. #4
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    Well, I'm not sure how to prove that If (m,n) = 1 then (2^m - 1, 2^n - 1) = 1 .. Can you help me, please?
    Last edited by helgamauer; November 14th 2010 at 08:40 AM.
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  5. #5
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