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Lucas balancing numbers

Kálmán Liptai — 2006

Acta Mathematica Universitatis Ostraviensis

A positive n is called a balancing number if 1 + 2 + ⋯ + ( n - 1 ) = ( n + 1 ) + ( n + 2 ) + ⋯ + ( n + r ) . We prove that there is no balancing number which is a term of the Lucas sequence.

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