Geodesic
Lucas balancing numbers
Communications in Mathematics, Tome 14 (2006) no. 1, pp. 43-47
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A positive $n$ is called a balancing number if \[1+2+\cdots +(n-1)=(n+1)+(n+2)+\cdots +(n+r).\] We prove that there is no balancing number which is a term of the Lucas sequence.
A positive $n$ is called a balancing number if \[1+2+\cdots +(n-1)=(n+1)+(n+2)+\cdots +(n+r).\] We prove that there is no balancing number which is a term of the Lucas sequence.
Classification : 11B39, 11D45, 11J86
Keywords: Baker method; Pell equations; recurrence sequences 
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Liptai, Kálmán. Lucas balancing numbers. Communications in Mathematics, Tome 14 (2006) no. 1, pp. 43-47. http://geodesic.mathdoc.fr/item/COMIM_2006_14_1_a6/

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