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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Catalan’s Conjecture: Another old Diophantine problem solved
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by Tauno Metsänkylä PDF
Bull. Amer. Math. Soc. 41 (2004), 43-57 Request permission

Abstract:

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.
References
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Additional Information
  • Tauno Metsänkylä
  • Affiliation: Department of Mathematics, University of Turku, FIN-20014 Turku, Finland
  • Email: taumets@utu.fi
  • Received by editor(s): March 5, 2003
  • Received by editor(s) in revised form: July 14, 2003
  • Published electronically: September 5, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 41 (2004), 43-57
  • MSC (2000): Primary 11D41, 00-02; Secondary 11R18
  • DOI: https://doi.org/10.1090/S0273-0979-03-00993-5
  • MathSciNet review: 2015449