蚀刻术
发表于 2025-3-27 00:37:16
The Nontrivial Solution,In this chapter, we present a different solution. It is due to W. McCallum . He reduces the problem to a Thue equation, which he solves by means of Skolem’s method. See for this method.
Corral
发表于 2025-3-27 03:41:55
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Cloudburst
发表于 2025-3-27 09:03:13
An Obstruction Group,Nonzero solutions to Catalan’s equation . naturally give rise to elements in certain obstruction groups. Mihăilescu’s theorems can be viewed as results about the size of the submodules generated by these elements. In this section, we introduce the notions and notations that are used in the remaining sections.
不幸的人
发表于 2025-3-27 12:00:00
Small , or ,,In this chapter, we present Mihăilescu’s proof of Theorem IV mentioned in chapter 1. The proof is by a .-adic argument. Let . be distinct odd primes.
轻推
发表于 2025-3-27 17:13:22
The Stickelberger Ideal,Let . be an odd prime and let .. denote a primitive .th root of unity.
或者发神韵
发表于 2025-3-27 20:28:45
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Gossamer
发表于 2025-3-27 23:51:40
The Minus Argument,In this chapter, we prove Theorem III of chapter 1. The proof is “Archimedean” in the sense that it exploits the fact that for any nonzero solution .,. of Catalan’s equation ., the absolute values of . and . are necessarily very large. This follows from Corollary 6.5 (iii). We use the notation introduced in chapter 7.
检查
发表于 2025-3-28 04:16:44
The Plus Argument I,In this chapter and chapter 14, we prove Theorem II of chapter 1. There are two main ingredients: the Runge method, exploited here, and Thaine’s theorem, which is used in chapter 14.
无关紧要
发表于 2025-3-28 09:23:46
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metropolitan
发表于 2025-3-28 14:24:47
The Plus Argument II,In this chapter, we prove Theorem II of chapter 1. The key ingredients are the results of chapter 12 and Francisco Thaine’s famous theorem , which is proved in chapter 16. Let . be odd primes and let . be a nonzero solution to Catalan’s equation ..