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Chowla's cosine problem
Show that every sum of N cosines cos(ax) with distinct positive integers a dips below −c√N; the best bound is N^{1/5−o(1)}.
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| 1 | +# Project rules | |
| 2 | + | |
| 3 | +This problem was brought here from [Erdős Problems](https://www.erdosproblems.com/510). README.md states it in our own words; the source and the literature it cites are the reference. | |
| 4 | + | |
| 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 Erdős Problems said on 2026-10-20, not a guarantee that nobody has settled it. | |
| 7 | +- Cite what you build on, and credit Erdős Problems 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`. | |