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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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Just FYI: "there are only a finite number of Fibonacci numbers that are the sum of two prime powers" is $\rm not$ the same as "there are an infinite number of Fibonacci numbers that are not the sum of two prime powers" –  anon Feb 2 '12 at 19:04
    
I know! Just that the covering system in above cited paper provides a kind of motivation whereas the S-unit equation thing proves the whole thing right away, therefore I am more in pursuit of the later. –  Nikhil Bellarykar Feb 2 '12 at 19:36
    
Also posted to MathOverflow, mathoverflow.net/questions/87364/… Nikhil, don't do that without notifying both sites. Better yet, don't do that. –  Gerry Myerson Feb 2 '12 at 23:26
    
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. –  Nikhil Bellarykar Feb 3 '12 at 18:55

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