- #1
meemoe_uk
- 125
- 0
Hi dudes, don't be put off by the clumsy notation here.
I was wondering about these particular exponent towers and this curious property of theirs...
Let p be a positive integer. Then the exponent tower, composed of p+1 parts each of value p^(1/p), equals p.
e.g. for p=2.
tower part = 2^(1/2)
(2^(1/2))^ ((2^(1/2))^(2^(1/2)))=2
bah, this looks clumsy, but it's concise written by hand, i.e. a 3 part exponent tower.
Anyway, I heard that it's difficult to prove any particular case for p, let alone the general case. I had a go myself for case p=2. I set x equals exponent tower and tried to show x=2, but I got nowhere.
Can anyone post the easiest proof for case p=2?, or any other case?
I was wondering about these particular exponent towers and this curious property of theirs...
Let p be a positive integer. Then the exponent tower, composed of p+1 parts each of value p^(1/p), equals p.
e.g. for p=2.
tower part = 2^(1/2)
(2^(1/2))^ ((2^(1/2))^(2^(1/2)))=2
bah, this looks clumsy, but it's concise written by hand, i.e. a 3 part exponent tower.
Anyway, I heard that it's difficult to prove any particular case for p, let alone the general case. I had a go myself for case p=2. I set x equals exponent tower and tried to show x=2, but I got nowhere.
Can anyone post the easiest proof for case p=2?, or any other case?