On the local structure of the set of values of Euler's function
Tom 199 / 2021
Acta Arithmetica 199 (2021), 103-109
MSC: Primary 11B83; Secondary 11B05, 11N32, 11N64.
DOI: 10.4064/aa200722-26-1
Opublikowany online: 4 March 2021
Streszczenie
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.
