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Re: [PrimeNumbers] Integer quotient

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  • Phil Carmody
    ... Proof: n+1
    Message 1 of 2 , Oct 1, 2006
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      --- Sebastian Martin <sebi_sebi@...> wrote:
      > Hello all:
      >
      > Prove:
      >
      > (2^(2^(2^n))-1)/(2^(2^(n+1))-1)
      >
      > Is integer for all n positive integer.

      Proof:
      n+1<=2^n
      QED.

      > More general:
      >
      > Is true?
      >
      > (k^(k^(k^n))-1)/(k^(k^(n+1))-1)
      >
      > Is integer for all k,n positive integers k>1

      Proof:
      n+1<=2^n
      QED.

      Phil

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