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I was looking up some stuff when I stumbled across S unit equations. It seems to me that they are quite helpful in number theory, as given in this paper.

http://faculty.nps.edu/pstanica/research/fiboprimeProcAMS.pdf

Here, the authors prove that there are only a finite number of Fibonacci numbers that are the sum of two prime powers. As an example, they exhibit a class where infinitely many Fibonacci numbers belong and are not the sum of two prime powers. While the example is produced using a covering system, the lemma cited is that of S unit equations. I looked up on net, but could not find a good introductory material on them.

Any help will be appreciated. Thanks in advance.

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    Ok, fine. I agree about notifying, but why do you say "better don't do that"? I posted this on MO because I did not get any answers here.2012-02-03

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