Let A be a set of natural numbers such that the set A+A contains no perfect squares. We prove that if the density d(A) exists, it is not larger than 2Γ5. ## 1999 Academic Press In this note we are concerned with a problem of Erdo s and Silverman (see ) who asked about the maximal density d max of
On Sets of Natural Numbers Whose Difference Set Contains No Squares
β Scribed by Pintz, J.; Steiger, W. L.; Szemeredi, E.
- Book ID
- 120095777
- Publisher
- Oxford University Press
- Year
- 1988
- Tongue
- English
- Weight
- 261 KB
- Volume
- s2-37
- Category
- Article
- ISSN
- 0024-6107
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π SIMILAR VOLUMES
A subset of the natural numbers is k-sum-free if it contains no solutions of the equation x 1 + } } } +x k = y, and strongly k-sum-free when it is l-sum-free for every l=2, ..., k. It is shown that every k-sum-free set with upper density larger than 1Γ(k+1) is a subset of a periodic k-sum-free set a
## Abstract In this paper, we study the problem of constructing sets of __s__ latin squares of order __m__ such that the average number of different ordered pairs obtained by superimposing two of the __s__ squares in the set is as large as possible. We solve this problem (for all __s__) when __m__