Displaying similar documents to “Distribution functions of the sequence ϕ ( m ) / m , m ( k , k + N ) as k , N go to infinity.”

Pseudoprime Cullen and Woodall numbers

Florian Luca, Igor E. Shparlinski (2007)

Colloquium Mathematicae

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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.