Lucas balancing numbers

Kálmán Liptai

Acta Mathematica Universitatis Ostraviensis (2006)

  • Volume: 14, Issue: 1, page 43-47
  • ISSN: 1804-1388

Abstract

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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.

How to cite

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Liptai, Kálmán. "Lucas balancing numbers." Acta Mathematica Universitatis Ostraviensis 14.1 (2006): 43-47. <http://eudml.org/doc/35161>.

@article{Liptai2006,
abstract = {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.},
author = {Liptai, Kálmán},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {Baker method; Pell equations; recurrence sequences; balancing numbers; Lucas numbers},
language = {eng},
number = {1},
pages = {43-47},
publisher = {University of Ostrava},
title = {Lucas balancing numbers},
url = {http://eudml.org/doc/35161},
volume = {14},
year = {2006},
}

TY - JOUR
AU - Liptai, Kálmán
TI - Lucas balancing numbers
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2006
PB - University of Ostrava
VL - 14
IS - 1
SP - 43
EP - 47
AB - 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.
LA - eng
KW - Baker method; Pell equations; recurrence sequences; balancing numbers; Lucas numbers
UR - http://eudml.org/doc/35161
ER -

References

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  1. Baker A., Davenport H., The equations 3 x 2 - 2 = y 2 and 8 x 2 - 7 = z 2 , , Quart. J. Math. Oxford (2) 20 (1969), 129–137. (1969) MR0248079
  2. Baker A., Wüstholz G., Logarithmic forms and group varieties, , J. reine angew. Math., 442 (1993), 19–62. (1993) MR1234835
  3. Behera A., Panda G. K., On the square roots of triangular numbers, , Fibonacci Quarterly, 37 No. 2 (1999), 98–105. (1999) Zbl0962.11014MR1690458
  4. Ferguson D. E., Letter to the editor, , Fibonacci Quarterly, 8 (1970), 88–89. (1970) 
  5. Liptai K., Fibonacci balancing numbers, , Fibonacci Quarterly 42 (2004), 330–340. Zbl1067.11006MR2110086
  6. Shorey T. N., Tijdeman R., Exponential diophantine equations, , Cambridge University Press, (1986). (1986) Zbl0606.10011MR0891406
  7. Szalay L., A note on the practical solution of simultaneous Pell type equations, , submitted to Comp. Math. 

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