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when I was in high school I could observe this relation

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  • Sam Shahrokhi
    Hello everybody:   Having used a nice observation, I have proved the following statement using Fermat s last  theorem: the nth root of 2 is not rational for
    Message 1 of 2 , Feb 22, 2009
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      Hello everybody:
       

      Having used a nice observation, I have proved the following statement using Fermat's last
       theorem: the nth root of 2 is not rational for n>3. my proof is: suppose the
       contrary then P & F integers exist st. 2^ (1/n)=(P/F). Hence
       (F^ n)+(F^ n)=P^ n and this is impossible by the Fermat's last theorem.
       
      Sincerely.
       
      Saeed Ranjbar





      [Non-text portions of this message have been removed]
    • David Broadhurst
      ... You were lucky to be at high school after Fermat s last theorem was proven :-) http://www.mathpath.org/proof/nthroot.irrat.htm gives the argument in Hardy
      Message 2 of 2 , Feb 22, 2009
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        --- In primenumbers@yahoogroups.com,
        Sam Shahrokhi <sam_jenetik26@...> wrote:

        > theorem: the nth root of 2 is not rational for n>3.
        > my proof is: suppose the contrary then P & F integers exist
        > st. 2^ (1/n)=(P/F). Hence (F^ n)+(F^ n)=P^ n and this is
        > impossible by the Fermat's last theorem.

        You were lucky to be at high school after Fermat's last
        theorem was proven :-)

        http://www.mathpath.org/proof/nthroot.irrat.htm
        gives the argument in Hardy and Wright that
        N^(1/m) is irrational, unless N is the m-th power of an integer.

        David
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