Pseudoprime Cullen and Woodall numbers

Florian Luca, and Igor E. Shparlinski. "Pseudoprime Cullen and Woodall numbers." Colloquium Mathematicae 107.1 (2007): 35-43. <http://eudml.org/doc/283410>.

@article{FlorianLuca2007,
abstract = {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.},
author = {Florian Luca, Igor E. Shparlinski},
journal = {Colloquium Mathematicae},
keywords = {pseudoprime number; Cullen number; Woodall number},
language = {eng},
number = {1},
pages = {35-43},
title = {Pseudoprime Cullen and Woodall numbers},
url = {http://eudml.org/doc/283410},
volume = {107},
year = {2007},
}

TY - JOUR
AU - Florian Luca
AU - Igor E. Shparlinski
TI - Pseudoprime Cullen and Woodall numbers
JO - Colloquium Mathematicae
PY - 2007
VL - 107
IS - 1
SP - 35
EP - 43
AB - 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.
LA - eng
KW - pseudoprime number; Cullen number; Woodall number
UR - http://eudml.org/doc/283410
ER -