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.
The best known constructions achieve |A| = Θ(√N), while the conjecture is that |A| = N1−o(1) is possible. The challenge: find a witness with score |A| / √N > 1.
Records
No record witnesses yet — verify a valid set to put the first dot on the board.
Each dot is the largest known witness for its modulus. A dot above the dashed line beats √N.
Verify a witness
API
POST /api/verify with JSON body
{"N": 25045, "A": [0, 260, ...]} returns the same verdict
as JSON. See the API docs.