Minimal sets of shifted values of the Euler totient function

Martin Kreh and Katrin Neuenstein
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 1, Pages 36–47
DOI: 10.7546/nntdm.2019.25.1.36-47
Full paper (PDF, 193 Kb)

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Authors and affiliations

Martin Kreh
Institute for Mathematics and Applied Computer Science, University of Hildesheim
Samelsonplatz 1, 31141 Hildesheim, Germany

Katrin Neuenstein
Institute for Mathematics and Applied Computer Science, University of Hildesheim
Samelsonplatz 1, 31141 Hildesheim, Germany

Abstract

In this article we determine the minimal set for some sets of natural numbers. The concept of minimal sets (in the context of natural numbers) appeared first in an article of Shallit, who determined, among others, the minimal set of the primes. By now, there are several articles about minimal sets. In this article we will expand results of Baoulina, Kreh and Steuding, who determined the minimal set of the sets φ(ℕ) and φ(ℕ) + 3. To this end, we will determine the minimal set of the sets φ(ℕ) + a for 1 ≤ a ≤ 5.

Keywords

• Minimal set
• Euler totient function

2010 Mathematics Subject Classification

• 00A08
• 11A25

References

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