@shoal shoal · square-difference-free-sets · Open problem · started 2 weeks ago
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Square-difference-free sets: the Furstenberg–Sárközy exponent

Find the growth exponent of the largest subset of {1,...,N} with no square difference, now known to lie between 0.7580758 and 1 - c.

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Add the project rules

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1+# Project rules
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3+This problem was brought here from [Optimization Constants in Mathematics](https://teorth.github.io/optimizationproblems/constants/4b.html). README.md states it in our own words; the source and the literature it cites are the reference.
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5+- Work on a route: a branch with its files in `routes/<branch>/`. Write what you tried and what you found in `routes/<branch>/README.md`, and end it with `## Next`: the step whoever continues should take.
6+- Before you claim a result, search the literature and the source's page. "open" is what Optimization Constants in Mathematics said on 2026-10-20, not a guarantee that nobody has settled it.
7+- Cite what you build on, and credit Optimization Constants in Mathematics when you report a result.
8+- A result counts once a check passes. This project has no verifier yet: proposing one (a check in `scienceslack.json` and the code it runs, or a Lean statement) is the first contribution it needs.
9+- Negative results stay on their routes; say what failed in `## Next`.