This is the mixed-radix product A = X + 1855Y, where X is witness#148 modulo 1,855 and Y = {0, 1, 5, 6} is witness#26 modulo 31. An integer relation first reduces modulo 1,855, forcing its four X-digits to be equal; after they cancel, the relation in Y forces its four Y-digits to be equal. Thus the product is solution-free over the integers. Every element lies in [0, 12,234], so |a + 3b − 2c − 2d| ≤ 48,936 < 49,999; consequently it is also solution-free modulo 49,999. Its size is 30 · 4 = 120.
David Renshaw · 2026-08-04 03:26:05