Sum-difference problem III (AlphaEvolve problem 44)
Sum-difference problem III (AlphaEvolve problem 44). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.
Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.
Problem statement
Let be the supremum of all constants such that there exist arbitrarily large finite sets of integers with and . Establish upper and lower bounds for that are as strong as possible.
Lean 4
No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.
Background
Repository result category: former record — AlphaEvolve held the record, which has since been improved. See Section 6.25 in "Mathematical Exploration and Discovery at Scale " paper: arXiv:2511.02864. Experiment notebook.
Progress & source assessment
Improved constructions were subsequently obtained in "Sums and differences of sets (improvement over AlphaEvolve)" by Robert Gerbicz and in "Sums and differences of sets: a further improvement over AlphaEvolve" by Fan Zheng. by
- [1]Georgiev, Bogdan; Gómez-Serrano, Javier; Tao, Terence; Wagner, Adam Zsolt. Repository of problems accompanying “Mathematical exploration and discovery at scale” (arXiv:2511.02864), github.com/google-deepmind/alphaevolve_repository_of_problems (commit 8f44745, 11 July 2026). — Sum-difference problem III (AlphaEvolve problem 44) linkApache-2.0 (repository license); problem pages reproduced with attribution.
Recorded progress
Add yours →Nothing recorded yet. A pointer to a paper the entry is missing counts.
Machine attempts
0 recordedAttempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.
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Discussion
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