witness #1661

N: 43,050
|A|: 140
exponent log |A| / log N: 0.4631

status: current record for this modulus
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-08 03:53:44 UTC

Elements (140)

0, 14, 45, 47, 59, 61, 82, 88, 96, 102, 168, 172, 182, 186, 287, 301, 332, 334, 346, 348, 369, 375, 383, 389, 455, 459, 469, 473, 1435, 1449, 1480, 1482, 1494, 1496, 1517, 1523, 1531, 1537, 1603, 1607, 1617, 1621, 1722, 1736, 1767, 1769, 1781, 1783, 1804, 1810, 1818, 1824, 1890, 1894, 1904, 1908, 8323, 8337, 8368, 8370, 8382, 8384, 8405, 8411, 8419, 8425, 8491, 8495, 8505, 8509, 8897, 8911, 8942, 8944, 8956, 8958, 8979, 8985, 8993, 8999, 9065, 9069, 9079, 9083, 9758, 9772, 9803, 9805, 9817, 9819, 9840, 9846, 9854, 9860, 9926, 9930, 9940, 9944, 10332, 10346, 10377, 10379, 10391, 10393, 10414, 10420, 10428, 10434, 10500, 10504, 10514, 10518, 25543, 25557, 25588, 25590, 25602, 25604, 25625, 25631, 25639, 25645, 25711, 25715, 25725, 25729, 26978, 26992, 27023, 27025, 27037, 27039, 27060, 27066, 27074, 27080, 27146, 27150, 27160, 27164

Commentary

Mixed-radix sum-set construction from the record witnesses for N=287 (size 14) and N=150 (size 10): A = A_287 + 287 A_150 in Z/(287*150). Validity follows by reducing any solution first mod 287, forcing the 287-digits equal, then mod 150 on the remaining digits.

last edited by Yongxi (Aaron) Lin at 2026-08-08 03:53:44 UTC · history