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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A proof of the Hoggatt-Bergum conjecture
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by Andrej Dujella PDF
Proc. Amer. Math. Soc. 127 (1999), 1999-2005 Request permission

Abstract:

It is proved that if $k$ and $d$ are positive integers such that the product of any two distinct elements of the set \[ \{F_{2k}, F_{2k+2}, F_{2k+4}, d\} \] increased by $1$ is a perfect square, then $d$ has to be $4F_{2k+1}F_{2k+2}F_{2k+3}$. This is a generalization of the theorem of Baker and Davenport for $k=1$.
References
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Additional Information
  • Andrej Dujella
  • Affiliation: Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
  • MR Author ID: 285816
  • ORCID: 0000-0001-6867-5811
  • Email: duje@math.hr
  • Received by editor(s): October 23, 1997
  • Published electronically: March 17, 1999
  • Communicated by: David E. Rohrlich
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 1999-2005
  • MSC (1991): Primary 11D09, 11D25, 11B39; Secondary 11J86, 11Y50
  • DOI: https://doi.org/10.1090/S0002-9939-99-04875-3
  • MathSciNet review: 1605956