3
$\begingroup$

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.

  • 0
    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"*2012-02-02
  • 0
    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.2012-02-02
  • 0
    Also posted to MathOverflow, http://mathoverflow.net/questions/87364/a-good-introduction-to-s-unit-equations Nikhil, don't do that without notifying both sites. Better yet, don't do that.2012-02-02
  • 1
    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

0 Answers 0