On an inequality about Euler’s totient function

Cheng-Ting Wang
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 31, 2025, Number 2, Pages 299–304
DOI: 10.7546/nntdm.2025.31.2.299-304
Full paper (PDF, 273 Kb)

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Authors and affiliations

Cheng-Ting Wang
Independent researcher
2F., No. 382, Daye Rd., Beitou Dist., Taipei City 112029, Taiwan

Abstract

In this paper, we show that when is a primorial and is Euler’s totient function, the inequality holds for all positive integer

Keywords

• Euler’s totient function
• Prime numbers
• Primorials

2020 Mathematics Subject Classification

• 11A25
• 11A41

References

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6. Rosser, B. (1939). The n-th prime is greater than n log n. Proceedings of The London Mathematical Society, s2–45(1), 21–44.
7. Rosser, B. (1941). Explicit bounds for some functions of prime numbers. American Journal of Mathematics, 63(1), 211–232.

Manuscript history

• Received: 21 October 2024
• Revised: 16 April 2025
• Accepted: 13 May 2025
• Online First: 29 May 2025

Copyright information

Ⓒ 2025 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).