On the additive completion of squares. II (Q1183256)
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scientific article; zbMATH DE number 33015
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the additive completion of squares. II |
scientific article; zbMATH DE number 33015 |
Statements
On the additive completion of squares. II (English)
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28 June 1992
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[Part I, cf. the first author, J. Number Theory 29, No. 1, 10-12 (1988; Zbl 0645.10047).] Let \(B\) be a set of integers such that every \(n\leq N\) can be written as the sum of an element from \(B\) and a perfect square. It is shown that \(| B| \geq 1.245\sqrt{N}\), thus improving the constant in the estimate \(| B|\geq 1.15\sqrt{N}\) due to the first author.
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representation of integers
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sum of an integer and a perfect square
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