Does Mihailescu's theorem use the infinitude of primes?

In summary, the conversation discusses the use of the infinitude of primes in proving Catalan's conjecture. The conversation also mentions the difficulty in determining which theorems the infinitude of primes is a necessary part of. The availability of a thesis and a paper on the topic is also mentioned.
  • #1
DaTario
1,093
45
TL;DR Summary
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
 
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  • #2
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.
 
  • #3
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.
 

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