Does Mihailescu's theorem use the infinitude of primes?

  • Level: Graduate 
  • Thread starter Thread starter DaTario
  • Start date Start date
  • Tags Tags
    Primes Theorem
Join the discussion
Registration is free. Start your own thread to ask a follow-up.
Sign up Log in
2 replies · 2K views
DaTario
Messages
1,097
Reaction score
46
TL;DR
Hi all,
I would like to know if in proving the Catalan's conjecture Preda Mihailescu used the infinitude of primes.
Hi all,
I would like to know if in proving the Catalan's conjecture Preda Mihailescu used the infinitude of primes.

Best wishes,
DaTario
 
Mathematics news on Phys.org

Discussion

Do you have a reference? I guess not many people have actually read the proof. Proofs of this kind often prove upper bounds for possible solutions and check the ones below. The infiniteness of primes is so deeply woven into number theory, that it is probably impossible to figure out which theorems it is actually a necessary part of. Nobody will ever have bothered otherwise.
 
I had access to this thesis, but to his paper I haven't.

He seems to be worried with two prime numbers (the exponents) and wether one of them divides the other or not. But I am really not sure.
 
Attachments

Similar threads

Graduate What conditions does Mihăilescu's theorem place on x, y, a and b?
  • e2m2a
  • · Replies 1 ·
  • General Math
Replies
1