The cardinality of a set containing the pairwise sums of a fixed number of integers
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918476901253120 |
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| author | van Doorn, Wouter |
| author_facet | van Doorn, Wouter |
| contents | Revisiting a $50$-year-old estimate of Choi, Erdős and Szemerédi, we show that if $A \subseteq \{1, 2, \ldots, 2n\}$ satisfies $|A| \ge n + 1.2 \cdot 10^8$, then there exist five distinct integers whose pairwise sums are all contained in $A$. In order to guarantee pairwise sums of three or four integers instead, we show that one can replace the constant $1.2 \cdot 10^8$ by $1$ or $3$ respectively, which are both optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00040 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The cardinality of a set containing the pairwise sums of a fixed number of integers van Doorn, Wouter Number Theory Revisiting a $50$-year-old estimate of Choi, Erdős and Szemerédi, we show that if $A \subseteq \{1, 2, \ldots, 2n\}$ satisfies $|A| \ge n + 1.2 \cdot 10^8$, then there exist five distinct integers whose pairwise sums are all contained in $A$. In order to guarantee pairwise sums of three or four integers instead, we show that one can replace the constant $1.2 \cdot 10^8$ by $1$ or $3$ respectively, which are both optimal. |
| title | The cardinality of a set containing the pairwise sums of a fixed number of integers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2605.00040 |