The iterated Carmichael lambda function

2011/11/15 by Nick Harland, Harland, Nick
Mathematics · #Advanced Mathematical Identities #Advanced Topology and Set Theory #Combinatorics #Computer science #FOS: Mathematics #Function (biology) #Integer (computer science) #Iterated function #Lambda #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Modulo #Number Theory (math.NT) #Order (exchange) #Physics #Prime (order theory) #math.NT

paper · pdf · doi:10.48550/arxiv.1111.3667

arxiv created 2011/11/15 · openalex publication_date 2011/11/15 · arxiv updated 2011/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The Carmichael lambda function λ(n) is defined to be the smallest positive integer m such that a^m is congruent to 1 modulo n, for all a and n relatively prime. The function λ_k(n) is defined to be the kth iterate of λ(n). Previous results show a normal order for n/λ_k(n) where k=1,2. We will show a normal order for all k.

Related

• The number of iterates of the Carmichael lambda function required to reach 1
• The Asymptotic Behavior of Compositions of the Euler and Carmichael Functions
• Two problems on the distribution of Carmichael's lambda function
• Runs of integers with constant values of the Carmichael function
• The Arithmetic of Carmichael Quotients