On the local structure of the set of values of Euler's $\varphi $ function
Volume 199 / 2021
Acta Arithmetica 199 (2021), 103-109
MSC: Primary 11B83; Secondary 11B05, 11N32, 11N64.
DOI: 10.4064/aa200722-26-1
Published online: 4 March 2021
Abstract
Assuming the validity of Dickson’s conjecture, we show that the set $\mathcal {V}$ of values of 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.
