Number Theory
Number Theory
Number Theory
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Table of Contentsxxi16.4 Mihăilescu’s Fourth Theorem: p ≡ 1 (mod q) or q ≡ 1 (mod p)115916.4.1 Preliminaries on Commutative Algebra . . . . . . . . . . . . . . 115916.4.2 Preliminaries on the Plus Part . . . . . . . . . . . . . . . . . . . . . 116116.4.3 Cyclotomic Units and Thaine’s Theorem . . . . . . . . . . . . 116416.4.4 Preliminaries on Power Series . . . . . . . . . . . . . . . . . . . . . . 116616.4.5 Proof of Mihăilescu’s Fourth Theorem . . . . . . . . . . . . . . 116916.4.6 Conclusion: Proof of Catalan’s Conjecture . . . . . . . . . . . 1172Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1173Index of Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1182Index of Names . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1182General Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1189