Hi dudes, don't be put off by the clumsy notation here.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Wonderful exponent tower property!

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