2003/09/05 by Tauno Metsänkylä · 4 citations
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #History and Theory of Mathematics
paper · pdf · doi:10.1090/s0273-0979-03-00993-5
openalex publication_date 2003/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07
Catalan’s Conjecture predicts that 8 and 9 are the only consecutive perfect powers among positive integers. The conjecture, which dates back to 1844, was recently proven by the Swiss mathematician Preda Mihăilescu. A deep theorem about cyclotomic fields plays a crucial role in his proof. Like Fermat’s problem, this problem has a rich history with some surprising turns. The present article surveys the main lines of this history and outlines Mihăilescu’s brilliant proof.