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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On the distribution of the number of prime factors of sums $ a+b$


Authors: P. Erdős, H. Maier and A. Sárközy
Journal: Trans. Amer. Math. Soc. 302 (1987), 269-280
MSC: Primary 11N60
MathSciNet review: 887509
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Abstract: We continue a series of investigations by A. Balog and two of the authors (P. Erdös and A. Sárközy) on the arithmetic properties of the elements $ a + b$, where $ a \in {\mathbf{A}}$, $ b \in {\mathbf{B}}$, $ {\mathbf{A}}$ and $ {\mathbf{B}}$ "dense sequences."

The present paper transfers the famous Erdös-Kac theorem on the normal distribution of the number of distinct prime factors of integers to such "sum sequences."


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0887509-X
PII: S 0002-9947(1987)0887509-X
Article copyright: © Copyright 1987 American Mathematical Society