Carmichael numbers in the sequence (k2ⁿ+1)_{n≥ 1}

2013/05/15 by Javer Cilleruelo, Cilleruelo, Javer, Florian Luca +4
Mathematics · #Advanced Mathematical Identities #Advanced Mathematical Theories #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1305.3580

25 pages

arxiv created 2013/05/15 · openalex publication_date 2013/05/15 · arxiv updated 2013/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for each odd number k, the sequence (k2ⁿ+1)_{n≥ 1} contains only a finite number of Carmichael numbers. We also prove that k=27 is the smallest value for which such a sequence contains some Carmichael number.

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