A proof of the Hoggatt-Bergum conjecture

Author:
Andrej Dujella

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

Published electronically:
March 17, 1999

MathSciNet review:
1605956

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that if and are positive integers such that the product of any two distinct elements of the set

increased by is a perfect square, then has to be . This is a generalization of the theorem of Baker and Davenport for .

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Additional Information

**Andrej Dujella**

Affiliation:
Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia

Email:
duje@math.hr

DOI:
https://doi.org/10.1090/S0002-9939-99-04875-3

Keywords:
Fibonacci numbers,
property of Diophantus,
simultaneous Pellian equations,
linear form in logarithms,
Baker-Davenport reduction procedure

Received by editor(s):
October 23, 1997

Published electronically:
March 17, 1999

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 1999
American Mathematical Society