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arXiv · 2001.05944

On the local structure of the set of values of Euler's $\varphi$ function

Jean-Marc Deshouillers·Pramod Eyyunni·Sanoli Gun
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Abstract

Assuming the validity of Dickson's conjecture, we show that the set $\mathcal{V}$ of values of the Euler's totient function $\varphi$ contains arbitrarily large arithmetic progressions with common difference 4. This leads to the question of proving unconditionally that this set $\mathcal{V}$ has a positive upper Banach density.

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Jean-Marc Deshouillers, Pramod Eyyunni, Sanoli Gun. 2020-01-16. On the local structure of the set of values of Euler's $\varphi$ function. https://arxiv.org/abs/2001.05944

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