Sums and differences of sets (improvement over AlphaEvolve)
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910961550491648 |
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| author | Gerbicz, Robert |
| author_facet | Gerbicz, Robert |
| contents | On May 14, 2025, DeepMind announced that AlphaEvolve, a large language model applied to a set of mathematical problems, had matched or exceeded the best known bounds on several problems. In the case of the sum and difference of sets problem, AlphaEvolve, using a set of $54265$ integers, improved the known lower bound of $θ=1.14465$ to $θ=1.1584$. In this paper, we present an improved bound $θ=1.173050$ using an explicit construction of a U set that contains more than $10^{43546}$ elements. For fast integer and floating-point arithmetic, we used the (free) GMP library. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16105 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sums and differences of sets (improvement over AlphaEvolve) Gerbicz, Robert Number Theory 11B75 On May 14, 2025, DeepMind announced that AlphaEvolve, a large language model applied to a set of mathematical problems, had matched or exceeded the best known bounds on several problems. In the case of the sum and difference of sets problem, AlphaEvolve, using a set of $54265$ integers, improved the known lower bound of $θ=1.14465$ to $θ=1.1584$. In this paper, we present an improved bound $θ=1.173050$ using an explicit construction of a U set that contains more than $10^{43546}$ elements. For fast integer and floating-point arithmetic, we used the (free) GMP library. |
| title | Sums and differences of sets (improvement over AlphaEvolve) |
| topic | Number Theory 11B75 |
| url | https://arxiv.org/abs/2505.16105 |