## when I was in high school I could observe this relation

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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
Message 1 of 2 , Feb 22, 2009
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]
• ... 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
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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