The set of values of any finite iteration of Euler's \(\varphi\) function contains long arithmetic progressions

DOI10.4064/AA230601-7-9MaRDI QIDQ6595591

R. Balasubramanian, Sanoli Gun, Jean-Marc Deshouillers

Publication date: 30 August 2024

Published in: Acta Arithmetica (Search for Journal in Brave)

zbMATH Keywords

Dickson's conjectureBanach densitylong arithmetic progressioniterated values of Euler's totient \(\phi\) function

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Density, gaps, topology (11B05) Arithmetic progressions (11B25) Primes represented by polynomials; other multiplicative structures of polynomial values (11N32)

Cites Work

• On hypereven numbers and on \textit{Fermat's} numbers.
• A new extension of Dirichlet's theorem on prime numbers.
• On the local structure of the set of values of Euler’s $\varphi $ function

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