Binomial formulas via divisors of numbers

Karol Gryszka
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 4, Pages 122—128
DOI: 10.7546/nntdm.2021.27.4.122-128
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Authors and affiliations

Karol Gryszka
Institute of Mathematics, Pedagogical University of Kraków
Podchorążych 2, 30-084 Kraków, Poland

Abstract

The purpose of this note is to prove several binomial-like formulas whose exponents are values of the function ω(n) counting distinct prime factors of n.

Keywords

  • Divisor
  • Multiplicative function
  • Square-free number
  • Multinomial formula
  • Symmetric polynomial

2020 Mathematics Subject Classification

  • 11A25
  • 11C08

References

  1. Jakimczuk, R. (2018). On the function ω(n). International Mathematical Forum, 13(3), 107–116.
  2. Lang, S. (2002). Algebra, Graduate Texts in Mathematics, 211 (Revised third ed.), New York: Springer-Verlag.
  3. Vassilev-Missana, M. V. (2019). New form of the Newton’s binomial theorem. Notes on Number Theory and Discrete Mathematics, 25(1), 48–49.

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Cite this paper

Gryszka, K. (2021). Binomial formulas via divisors of numbers. Notes on Number Theory and Discrete Mathematics, 27(4), 122-128, doi: 10.7546/nntdm.2021.27.4.122-128/.

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