On the number of prime factors of integers of the form ab + 1
K. Győry, A. Sárközy, C. L. Stewart (1996)
Acta Arithmetica
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Displaying similar documents to “On prime factors of sums of integers I”
On the number of prime factors of integers of the form ab + 1
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Jan Turk (1977-1978)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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On integers with many small prime factors
R. Tijdeman (1973)
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P. Erdös, T. Shorey (1976)
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Prime divisors of some shifted products.
Levieil, Eric, Luca, Florian, Shparlinski, Igor E. (2005)
International Journal of Mathematics and Mathematical Sciences
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T. N. Shorey, R. Tijdeman (1976)
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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.
Positive integers such that .
Luca, Florian (2003)
Novi Sad Journal of Mathematics
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The divisors of integers II
R. Hall (1975)
Acta Arithmetica
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