2015/08/24 by Bernadette Faye, Florian Luca, Faye, Bernadette +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1508.05709
openalex publication_date 2015/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A composite positive integer n is Lehmer if ϕ(n) divides n-1, where ϕ(n) is the Euler's totient function. No Lehmer number is known, nor has it been proved that they don't exist. In 2007, the second author [7] proved that there is no Lehmer number in the Fibonacci sequence. In this paper, we adapt the method from [7] to show that there is no Lehmer number in the companion Lucas sequence of the Fibonacci sequence (Ln)n≥ 0 given by L0 = 2, L1 = 1 and Ln+2 = Ln+1 + Ln for all n≥ 0.