Rational ^ sqrt(5) = rational ?

  • Thread starter Gerenuk
  • Start date
  • #1
1,015
3
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 :(
 

Answers and Replies

  • #2
gel
533
5
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:

Related Threads on Rational ^ sqrt(5) = rational ?

  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
4
Views
6K
  • Last Post
Replies
1
Views
2K
Replies
8
Views
6K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
6
Views
5K
Top