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Math Help - prove tha if k/n

  1. #1
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    Unhappy prove tha if k/n

    Prove that if k and n are positive integers with n>k>1 such that k divides n, then ((2^k)-1) divides ((2^n)-1)
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    Quote Originally Posted by mandy123 View Post
    Prove that if k and n are positive integers with n>k>1 such that k divides n, then ((2^k)-1) divides ((2^n)-1)
    In general if k|n then a^k-1 divides a^n-1.
    This is because n=km thus a^{km}-1 = (a^k)^m - 1.
    Now use identity for factoring x^n - y^n.
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