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
Full paper (PDF, 193 Kb)

Details

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.