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Li GAO; Xinxin LI

doi:10.19789/j.1004-9398.2026.02.006

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Publishing Language: Chinese | Open Access

The solvability of arithmetic function equation $φ_{e} (n) = Z (S L (n))$ $(e = 12)$

Li GAO^{¹^,²}, Xinxin LI^²(

)

College of Information Engineering, Xi'an Fanyi University, Xi'an Shaanxi 710105

College of Mathematics and Computer Science, Yan'an University, Yan'an Shaanxi 716000

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Abstract

Using definition and properties of the generalized Euler function and Smarandache LCM function, this paper discusses the integer solutions problems of equations involving generalized Euler functions $φ_{e} (n) = Z (S L (n)) (e = 12)$ .

Keywords

solvability generalized Euler function Smarandache LCM function positive integer solution

CLC number: O156 Document code: A

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Journal of Capital Normal University (Natural Science Edition)

Volume 47 Issue 2,
April 2026

Pages 38-45

DOI: 10.19789/j.1004-9398.2026.02.006

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Cite this article:

GAO L, LI X. The solvability of arithmetic function equation

φ_{e} (n) = Z (S L (n))

(e = 12)

. Journal of Capital Normal University (Natural Science Edition), 2026, 47(2): 38-45. https://doi.org/10.19789/j.1004-9398.2026.02.006

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Received: 20 November 2024

Published: 01 April 2026

This is an open access article under the CC BY-NC-ND 4.0 license (https://creativecommons.org/licenses/by-nc-nd/4.0/).

The solvability of arithmetic function equation φ e ( n ) = Z ( S L ( n ) ) ( e = 12 )

Abstract

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The solvability of arithmetic function equation $φ_{e} (n) = Z (S L (n))$ $(e = 12)$