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.


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.

So where can I find a good, relatively self-contained(not a major constraint though,this) introduction for S unit equations?

Any help will be appreciated. Thanks in advance.


Lang: Fundamentals of diophantine geometry,Ch. 8, or Bombieri and Gubler: Heights in Diophantine Geometry Ch. 5.

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