- 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] - --- In primenumbers@yahoogroups.com,

Sam Shahrokhi <sam_jenetik26@...> wrote:

> theorem: the nth root of 2 is not rational for n>3.

You were lucky to be at high school after Fermat's last

> 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.

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