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Rational ^ sqrt(5) = rational ?

  1. Aug 31, 2008 #1
    I've programmed an algorithm to numerically compute the logarithm of numbers in phinary base easily. I could avoid float multiplications if I can find a pair of rational numbers x and y such that
    [tex]x^{\sqrt{5}}=y[/tex]
    Is it possible?
    Probably not, but I cannot prove it :(
     
  2. jcsd
  3. Aug 31, 2008 #2

    gel

    User Avatar

    No, it isn't possible except for the obvious x=y=1. There's a http://en.wikipedia.org/wiki/Gelfond–Schneider_theorem" [Broken] which says that it's impossible.
     
    Last edited by a moderator: May 3, 2017
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