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Multiplicative functions k-additive on hexagonal numbers

  • Elchin Hasanalizade EMAIL logo , Poo-Sung Park and Emil Inochkin
Published/Copyright: October 24, 2025
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 75 Issue 5

Abstract

Let k ≥ 3 be an integer. We prove that the set H of all nonzero hexagonal numbers is a k-additive uniqueness set for the set of multiplicative functions. That is, if a multiplicative function fk satisfies a multivariate Cauchy functional equation

f k ( x 1 + x 2 + ⋯ + x k ) = f k ( x 1 ) + f k ( x 2 ) + ⋯ + f k ( x k )

for arbitrary x1,…,xk∈H , then fk is the identity function fk(n) = n for all n∈N . This extends the work of Kim et al. for k = 2.

Keywords: Additive uniqueness; multiplicative functions; hexagonal numbers
MSC 2010: Primary 11A25; Secondary 11B99

Funding statement: This research was supported by ADA University Faculty Research and Development Funds and by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIT) (NRF-2021R1A2C1092930)

Acknowledgement

The authors would like to thank the anonymous referee for his/her helpful comments.

  1. (Communicated by István Gaál)

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Received: 2024-12-31
Accepted: 2025-06-10
Published Online: 2025-10-24
Published in Print: 2025-10-27

© 2025 Mathematical Institute Slovak Academy of Sciences

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  1. Copies of monomorphic structures
  2. Endomorphism kernel property for extraspecial and special groups
  3. Sums of Tribonacci numbers close to powers of 2
  4. Multiplicative functions k-additive on hexagonal numbers
  5. Monogenic even cyclic sextic polynomials
  6. Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function
  7. Degree of independence in non-archimedean fields
  8. Remarks on some one-ended groups
  9. Some new characterizations of weights for hardy-type inequalities with kernels on time scales
  10. Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach
  11. Radius estimates for functions in the class 𝒰r(λ)
  12. Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions
  13. More q-congruences from Singh’s quadratic transformation
  14. Stability and controllability of cycled dynamical systems
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  16. Strong solution of a Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flows with surfactant
  17. Coincidence points via tri-simulation functions with an application in integral equations
  18. On Fong-Tsui conjecture and binormality of operators
  19. Riemannian maps of CR-submanifolds of Kaehler manifolds
  20. On structural numbers of topological spaces
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https://doi.org/10.1515/ms-2025-0074
Keywords for this article
Additive uniqueness; multiplicative functions; hexagonal numbers

Articles in the same Issue

  1. Copies of monomorphic structures
  2. Endomorphism kernel property for extraspecial and special groups
  3. Sums of Tribonacci numbers close to powers of 2
  4. Multiplicative functions k-additive on hexagonal numbers
  5. Monogenic even cyclic sextic polynomials
  6. Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function
  7. Degree of independence in non-archimedean fields
  8. Remarks on some one-ended groups
  9. Some new characterizations of weights for hardy-type inequalities with kernels on time scales
  10. Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach
  11. Radius estimates for functions in the class 𝒰r(λ)
  12. Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions
  13. More q-congruences from Singh’s quadratic transformation
  14. Stability and controllability of cycled dynamical systems
  15. Existence, uniqueness, and multiplicity of radially symmetric k-admissible solutions for k-hessian equations
  16. Strong solution of a Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flows with surfactant
  17. Coincidence points via tri-simulation functions with an application in integral equations
  18. On Fong-Tsui conjecture and binormality of operators
  19. Riemannian maps of CR-submanifolds of Kaehler manifolds
  20. On structural numbers of topological spaces
  21. The κ-Fréchet-Urysohn property for Cp(X) is equivalent to baireness of B1(X)
  22. Weighted pseudo S-asymptotically (ω, c)-periodic solutions to fractional stochastic differential equations
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