A good introduction to S unit equations - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T18:52:28Z http://mathoverflow.net/feeds/question/87364 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/87364/a-good-introduction-to-s-unit-equations A good introduction to S unit equations Nikhil Bellarykar 2012-02-02T19:48:24Z 2012-02-02T21:29:33Z <p>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.</p> <p><a href="http://faculty.nps.edu/pstanica/research/fiboprimeProcAMS.pdf" rel="nofollow">http://faculty.nps.edu/pstanica/research/fiboprimeProcAMS.pdf</a></p> <p>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.</p> <p>So where can I find a good, relatively self-contained(not a major constraint though,this) introduction for S unit equations?</p> <p>Any help will be appreciated. Thanks in advance.</p> http://mathoverflow.net/questions/87364/a-good-introduction-to-s-unit-equations/87375#87375 Answer by Felipe Voloch for A good introduction to S unit equations Felipe Voloch 2012-02-02T21:29:33Z 2012-02-02T21:29:33Z <p>Lang: Fundamentals of diophantine geometry,Ch. 8, or Bombieri and Gubler: Heights in Diophantine Geometry Ch. 5. </p>