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A proof of the Hoggatt-Bergum conjecture

Authors:	Andrej Dujella

Institution:	Department of Mathematics, University of Zagreb, Bijenicka cesta 30, 10000 Zagreb, Croatia

Abstract:	It is proved that if and are positive integers such that the product of any two distinct elements of the set $\begin{displaymath}\{F_{2k},\, F_{2k+2},\, F_{2k+4},\, d\} \end{displaymath}$ increased by is a perfect square, then has to be $4F_{2k+1}F_{2k+2}F_{2k+3}$ . This is a generalization of the theorem of Baker and Davenport for .

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

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