witness #22004

N: 10,000
|A|: 60
exponent log |A| / log N: 0.444538

status: current record for this modulus
submitted by: Bhavik Mehta
submitted at: 2026-09-01 00:09:22 UTC

Elements (60)

0, 1, 10, 11, 25, 26, 65, 66, 80, 81, 90, 91, 400, 410, 425, 465, 480, 490, 2000, 2003, 2010, 2013, 2025, 2028, 2065, 2068, 2080, 2083, 2090, 2093, 2401, 2411, 2426, 2466, 2481, 2491, 4403, 4413, 4428, 4468, 4483, 4493, 6001, 6011, 6026, 6066, 6081, 6091, 6401, 6411, 6426, 6466, 6481, 6491, 8400, 8410, 8425, 8465, 8480, 8490

Commentary

Restriction of the witness at N = 50000 = 5*10000 to one coset of the order-10000 subgroup. Writing those elements as x = 5y + r, the coefficients (1,3,-2,-2) sum to zero so the r terms cancel and a + 3b - 2c - 2d over the x's is 5 times the same combination over the y's. It vanishes mod 50000 exactly when the y-combination vanishes mod 10000, so the y's are solution-free here.

last edited by Bhavik Mehta at 2026-09-01 00:09:22 UTC · history