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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A problem in additive number theory


Author: Donald Quiring
Journal: Proc. Amer. Math. Soc. 38 (1973), 250-252
DOI: https://doi.org/10.1090/S0002-9939-1973-0309893-3
MathSciNet review: 0309893
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Abstract | References | Additional Information

Abstract: For every real number $ \alpha ,0 < \alpha < 1$, a sequence $ A = \{ {a_1},{a_2}, \cdots \} $ is constructed for which the density of $ A$ is $ \alpha $ and $ A$ has the following property: Given any $ n$ distinct positive integers $ \{ {b_1},{b_2}, \cdots ,{b_n}\} $ the sequence consisting of all numbers of the form $ {a_i} + {b_j}$ has density $ 1 - {(1 - \alpha )^n}$.


References [Enhancements On Off] (What's this?)

  • [1] P. Erdős and A. Rényi, On some applications of probability methods to additive number theoretic problems, Contributions to Ergodic Theory and Probability (Proc. Conf., Ohio State Univ., Columbus, Ohio, 1970) Springer, Berlin, 1970, pp. 37–44. MR 0276190


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0309893-3
Article copyright: © Copyright 1973 American Mathematical Society

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