The period of the Bell numbers modulo a prime

DOI10.1090/S0025-5718-10-02340-9zbMath1216.11028OpenAlexW2017365327MaRDI QIDQ3584850

Sangil Nahm, Peter L. Montgomery, Samuel S. jun. Wagstaff

Publication date: 30 August 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-10-02340-9

zbMATH Keywords

Bell numbersperiod modulo \(p\)

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Congruences; primitive roots; residue systems (11A07) Factorization; primality (11A51) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

Related Items (11)

Closed expressions for averages of set partition statistics ⋮ Bell numbers and Kurepa’s conjecture ⋮ Backward Touchard congruence ⋮ Extensions of set partitions and permutations ⋮ Artin-Schreier, Erdős, and Kurepa’s conjecture ⋮ The largest singletons of set partitions ⋮ Some primitive elements for the Artin-Schreier extensions of finite fields ⋮ Unnamed Item ⋮ Bell numbers modulo a prime number, traces and trinomials ⋮ Divisibility properties of the \(r\)-Bell numbers and polynomials ⋮ Infinitely Many Twin Prime Polynomials of Odd Degree

Cites Work

• The Least Prime in Certain Arithmetic Progressions
• A Heuristic Asymptotic Formula Concerning the Distribution of Prime Numbers
• ABOUT THE PERIOD OF BELL NUMBERS MODULO A PRIME
• Minimum Periods, Modulo p, of First-Order Bell Exponential Integers
• Arithmetic properties of Bell numbers to a composite modulus I
• Divisors of Mersenne Numbers
• Aurifeuillian factorizations and the period of the Bell numbers modulo a prime
• Numbers Generated by the Function e e x-1

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