Mihailescu’s paper has now been verified as correct and proof of Catalan’s conjecture (Mihailescu 2004; Metsänkylä 2003).
This manuscript was reportedly sent on April 2002 to several mathematicians, (Poorten 2002) along with an expository paper / summary by Yuri Bilu (Bilu and Collectif 2004).
As usual in mathematics and science, the proof wasn’t created in a vacuum. There had been several papers on possible exceptions, special cases and conditions for the conjecture to hold (Weisstein 2002).
References and Bibliography
Bilu, Yuri, and Collectif. 2004. “Catalan’s Conjecture.” In Séminaire Bourbaki : Volume 2002/2003, Exposés 909-923, 1–26. Astérisque 294. Paris: Association des amis de Nicolas Bourbaki, Société mathématique de France. http://www.numdam.org/item/SB_2002-2003__45__1_0.
Metsänkylä, Tauno. 2003. “Catalan’s Conjecture: Another Old Diophantine Problem Solved.” Bulletin of the American Mathematical Society 41 (01): 43–58. https://doi.org/10.1090/s0273-0979-03-00993-5.
Mihailescu, P. 2004. “Primary Cyclotomic Units and a Proof of Catalans Conjecture.” Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal) 2004 (572). https://doi.org/10.1515/crll.2004.048.
Poorten, Alf van der. 2002. “Concerning: Catalan’s Conjecture Proved?” May 5, 2002. https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;1a7d7d4.0205&S=.
Weisstein, Eric W. 2002. “MathWorld Headline News—Draft Proof of Catalan’s Conjecture Circulated.” May 5, 2002. https://mathworld.wolfram.com/news/2002-05-05/catalan/.
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