We investigate a number of questions concerning representations of a set of numbers as sums of subsets of some other set. In particular, we obtain several results on the possible sizes of the second set when the first set consists of a geometric sequence of integers, partially answering a generalisa
On Natural Numbers as Sums of Consecutiveh-th Powers
โ Scribed by Richard Warlimont
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 321 KB
- Volume
- 68
- Category
- Article
- ISSN
- 0022-314X
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๐ 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 1ร(k+1) is a subset of a periodic k-sum-free set a
Let Nรฐnร be the set of all integers that can be expressed as a sum of reciprocals of distinct integers 4n: Then we prove that for sufficiently large n; which improves the lower bound given by Croot. # 2002 Elsevier Science (USA)
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