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(1992)
On some conjectures of Erdo% s in AsteT risque, I'
Paul Erdös, G. Tenenbaum (1999)
Ensembles de multiples de suites finiesDiscret. Math., 200
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P. Shiu (1980)
A Brun-Titschmarsh theorem for multiplicative functions.Journal für die reine und angewandte Mathematik (Crelles Journal), 1980
R. Hall (1996)
Sets of Multiples
(1992)
On some conjectures of Erdo% s in AsteU risque, I
Abstract Let q and N be integers, let a be an integer coprime to q , and let zN be defined implicitly by q=(logN)log22−zN√(log2N) . We show that for large N , an integer n has at least one divisor d with q ≤ d ≤ N and d ≡ a (mod q ) with probability approximately Φ( zN ), where Φ denotes the distribution function of the Gaussian Law. This solves a conjecture of Hall. 1991 Mathematics Subject Classification 11N25, 11N37. © London Mathematical Society
Bulletin of the London Mathematical Society – Oxford University Press
Published: May 1, 2000
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