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Math Help - a question on square-free numbers

  1. #1
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    a question on square-free numbers

    Suppose that 2^m-1 and 2^m+1 are both square-free numbers. Denote by \phi the Euler function, and \pi(n) the set of prime divisors of n. If \pi(\phi(2^m-1))\subseteq\pi(2^m+1)\cup\{2\}, and \pi(\phi(2^m+1))\subseteq\pi(2^m-1)\cup\{2\}, then whether or not m is 2,4?
    Last edited by rulin; April 28th 2010 at 10:06 PM.
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by rulin View Post
    Let 2^m-1 and 2^m+1 be both square-free numbers. Denote by \phi Euler function, and \pi(n) the set of prime divisors of n. If \pi(\phi(2^m-1))\subseteq\pi(2^m+1)\cup\{2\}, and \pi(\phi(2^m+1))\subseteq\pi(2^m-1)\cup\{2\}, whether or mot m=2,4?
    You should rephrase your question, your grammar is a bit off.
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