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Shift Balancing Numbers


Affiliations
1 Department of Mathematics, National Institute of Technology, Rourkela - 769 008, India
2 Department of Mathematics, Gayatri Vidya Parishad College of Engineering (A), Visakhapatnam - 530048, India
     

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For each positive integer k, the Diophantine equation (k+1)+(k+2)+···+(n−1) = (n+1)+(n+2)+···+(n+r) is studied

Keywords

Lancing Numbers, Lucas-Balancing Numbers, Gap Balancing Numbers, t−balancing Numbers.
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  • A. Behera and G. K. Panda, On the square roots of triangular numbers, Fibonacci Quart., 37(2) (1999), 98-105.
  • K. K. Dash and R. S. Ota, t−Balancing Numbers, Int. J. Contemp. Math. Sciences, 7 (2012), 1999- 2012.
  • R. K. Davala and G. K. Panda, On sum and ratio formulas for balancing numbers, J. Ind. Math. Soc., 82(1-2) (2015), 23-32.
  • R. P. Finkelstein, The House Problem, Amer. Math. Monthly, 72 (1965), 1082-1088.
  • T. Kovács, K. Liptai and P. Olajos, On (a,b)-balancing numbers, Publ. Math. Debrecen, 77(3) (2010).
  • K. Liptai, Fibonacci Balancing Numbers, Fibonacci Quart., 42(4) (2004), 330-340.
  • K. Liptai, Lucas balancing numbers, Commun. Math., 14(1) (2006), 43-47.
  • R. A. Mollin, Fundamental number theory with applications, Boca Raton, CRC press, London (2004).
  • G. K. Panda and R. K. Davala, Perfect balancing numbers, Fibonacci Quart., 53(3) (2015), 261-264.
  • G. K. Panda and P. K. Ray, Cobalancing numbers and cobalancers, Internat. J. Math. Math. Sci., 8 (2005), 1189-1200.
  • G. K. Panda, Some fascinating properties of balancing numbers, In Proc. of Eleventh Internat. Conference on Fibonacci Numbers and Their Applications, Cong. Numerantium, 194, (2009), 185-189.
  • G. K. Panda and A. K. Panda, Almost balancing numbers, J. Ind. Math. Soc., 82(3-4) (2015), 147-156.
  • G. K. Panda and S. S. Rout, Periodicity of balancing numbers, Acta. Math. Hungar., 143(2) (2014), 274-286.
  • S. S. Rout and G. K. Panda, k-gap balancing numbers, Mathematika, 70(1) (2015), 109-121.
  • S. S. Rout, R. K. Davala and G. K. Panda, Stability of balancing sequence modulo p, Unif. Distrib. Theory, 10(2) (2015), 77-91.

Abstract Views: 32

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  • Shift Balancing Numbers

Abstract Views: 32  |  PDF Views: 1

Authors

S. G. Rayaguru
Department of Mathematics, National Institute of Technology, Rourkela - 769 008, India
G. K. Panda
Department of Mathematics, National Institute of Technology, Rourkela - 769 008, India
R. K. Davala
Department of Mathematics, Gayatri Vidya Parishad College of Engineering (A), Visakhapatnam - 530048, India

Abstract


For each positive integer k, the Diophantine equation (k+1)+(k+2)+···+(n−1) = (n+1)+(n+2)+···+(n+r) is studied

Keywords


Lancing Numbers, Lucas-Balancing Numbers, Gap Balancing Numbers, t−balancing Numbers.

References





DOI: https://doi.org/10.18311/jims%2F2020%2F24872