A proof of the Hoggatt-Bergum conjecture
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- by Andrej Dujella PDF
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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