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Integer quotient

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  • Sebastian Martin
    Hello all: Prove: (2^(2^(2^n))-1)/(2^(2^(n+1))-1) Is integer for all n positive integer. More general: Is true? (k^(k^(k^n))-1)/(k^(k^(n+1))-1) Is integer for
    Message 1 of 2 , Sep 30, 2006
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      Hello all:

      Prove:

      (2^(2^(2^n))-1)/(2^(2^(n+1))-1)

      Is integer for all n positive integer.

      More general:

      Is true?

      (k^(k^(k^n))-1)/(k^(k^(n+1))-1)

      Is integer for all k,n positive integers k>1


      Sincerely
      Sebastián Martín Ruiz

      http://perso.wanadoo.es/smaranda/








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    • Phil Carmody
      ... Proof: n+1
      Message 2 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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