Some Number-Theoretic Products

Authors

  • Narakorn Rompurk Kanasri Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand
  • Arlisa Janjing Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand

Keywords:

Arithmetic function, Euler phi-function, Möbius function, Product form of the Möbius inversion formula

Abstract

For a positive integer n, let P(n) and P′ (n) be the products of all elements in the finite sets {x: 1 ≤ x ≤ n, (x, n) = 1} and {x : 1 ≤ x ≤ n/2, (x, n) = 1}, respectively. In this article, we verify the formula for P(n) and use it to establish the formula for P′ (n). Explicit formulae for both P (pa) and P′ (pa), where pa is a prime power, are also derived.

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Published

2022-12-31

How to Cite

Narakorn Rompurk Kanasri, & Arlisa Janjing. (2022). Some Number-Theoretic Products. Science & Technology Asia, 27(4), 228–235. Retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/247953

Issue

Vol.27 No.4 (October-December 2022)

Section

Physical sciences

License

Copyright (c) 2022 Science & Technology Asia

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