József Sándor and Krassimir T. Atanassov

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 25, 2019, Number 4, Pages 8–15

DOI: 10.7546/nntdm.2019.25.4.8-15

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## Details

### Authors and affiliations

József Sándor

*Department of Mathematics, Babes–Bolyai University
Str. Kogalniceanu 1, 400084 Cluj-Napoca, Romania
*

Krassimir T. Atanassov

*Department of Bioinformatics and Mathematical Modelling
IBPhBME – Bulgarian Academy of Sciences,
Acad. G. Bonchev Str. Bl. 105, Sofia-1113, Bulgaria*

### Abstract

A new proof of solvability of equations

and

for are given. Connections with related problems and inequalities are pointed out, too.

### Keywords

- Arithmetic function
- Balanced number
- Inequality
- Sum of divisors of a number

### 2010 Mathematics Subject Classification

- 11A25
- 26D15

### References

- Sandor, J. (1990). An application of the Jensen–Hadamard inequality, Nieuw Arch. Wiskunde, 4 (8), 63–66.
- Sandor, J., Mitrinovic, D. S. & Crstici, B. (2006). Handbook of Number Theory, Vol. 1,

Springer. - Sandor, J. (2008). On equation Octogon Math. Mag., 16 (1), 288–290.
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- Sandor, J. (2009). A double-inequality for , Octogon Math. Mag., 17 (1), 285–287.
- Sandor, J. (2009). A better lower bound for , Octogon Math. Mag., 17 (2), 767–768.
- Sandor, J. & Kovacs, L. (2009). An inequality for the number of divisors of , Octogon Math. Mag., 17 (2), 746–750.
- Sandor, J. (2014). An arithmetic inequality, An. St. Univ. Ovidius Constanta, 22 (1), 257–261.
- Subbarao, M. V. (1963). Balanced numbers, Solution of Problem E558, Amer. Math. Monthly, 70, 1009–1010.
- Vassilev-Missana, M., & Atanassov, K. (2007). A new point of view on perfect and other similar numbers, Advanced Studies on Contemporary Mathematics, 15 (2), 153–169.

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## Cite this paper

APASándor, J. & Atanassov, K. (2019). A note on balanced numbers. Notes on Number Theory and Discrete Mathematics, 25(4), 8-15, doi: 10.7546/nntdm.2019.25.4.8-15.

ChicagoSándor, József and Krassimir Atanassov. (2019). “A Note on Balanced Numbers.” Notes on Number Theory and Discrete Mathematics. Notes on Number Theory and Discrete Mathematics 25, no. 4 (2019): 8-15, doi: 10.7546/nntdm.2019.25.4.8-15.

MLASándor, József and Krassimir Atanassov. (2019). “A Note on Balanced Numbers.” Notes on Number Theory and Discrete Mathematics 25.4 (2019): 8-15. Print, doi: 10.7546/nntdm.2019.25.4.8-15.