Fix a modulus N and look for a large set A ⊆ ℤ/Nℤ containing no nontrivial solutions to
a + 3b ≡ 2c + 2d (mod N)
with a, b, c, d ∈ A. A solution is trivial when a = b = c = d.
In a 1993 paper, Imre Z. Ruzsa suggested that |A| = N1−o(1) could be achievable. Our challenge: find an explicit witness with |A| > √N.
October 2026 update: Hametner and Solymosi proved that |A| ≥ N0.5608−o(1) is achievable, but their construction only beats √N for N much larger than 50,000.
Each dot is the largest known witness for its modulus. A dot above the dashed line beats √N.
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Submit a witness
API
POST /api/verify with JSON body
{"N": 25045, "A": [0, 260, ...]} returns the same verdict
as JSON. See the API docs.