Pseudoprime Cullen and Woodall numbers

• Autorzy: Florian Luca , Igor E. Shparlinski
• Języki publikacji: EN

Abstrakty

EN

We show that if a > 1 is any fixed integer, then for a sufficiently large x>1, the nth Cullen number Cₙ = n2ⁿ +1 is a base a pseudoprime only for at most O(x log log x/log x) positive integers n ≤ x. This complements a result of E. Heppner which asserts that Cₙ is prime for at most O(x/log x) of positive integers n ≤ x. We also prove a similar result concerning the pseudoprimality to base a of the Woodall numbers given by Wₙ = n2ⁿ - 1 for all n ≥ 1.

Kategorie tematyczne

• 11N25: Distribution of integers with specified multiplicative constraints
• 11B83: Special sequences and polynomials
• 11A07: Congruences; primitive roots; residue systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 107
• Numer: 1
• Strony: 35-43

Daty

wydano

2007

Twórcy

autor

Florian Luca

• Instituto de Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, México

autor

Igor E. Shparlinski

• Department of Computing, Macquarie University, Sydney, NSW 2109, Australia

Identyfikatory

DOI

10.4064/cm107-1-5