a + 3b = 2c + 2d

Ruzsa’s genus-one problem

Fix a modulus N and look for a large set Aℤ/Nℤ containing no nontrivial solutions to

a + 3b ≡ 2c + 2d (mod N)

with a, b, c, dA. 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.