2018/06/29 by Dominik Burek, Burek, Dominik, Błażej Żmija +1 · 1 citation
Computer Science · Mathematics · #Analytic Number Theory Research #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1806.11280
4 pages
arxiv created 2018/06/29 · openalex publication_date 2018/06/29 · arxiv updated 2018/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A composite positive integer n has the Lehmer property if ϕ(n) divides n-1, where ϕ is an Euler totient function. In this note we shall prove that if n has the Lehmer property, then n≤ 2^2K-2^2K-1, where K is the number of prime divisors of n. We apply this bound to repunit numbers and prove that there are at most finitely many numbers with the Lehmer property in the set \\fracgn-1g-1 | n,g∈ℕ, ν2(g)+ν2(g+1)≤ L \, where ν2(g) denotes the highest power of 2 that divides g, and L≥ 1 is a fixed real number.