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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A problem in additive number theory
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by Donald Quiring
Proc. Amer. Math. Soc. 38 (1973), 250-252
DOI: https://doi.org/10.1090/S0002-9939-1973-0309893-3
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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
  • 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
Bibliographic Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 38 (1973), 250-252
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0309893-3
  • MathSciNet review: 0309893