Ruzsa’s genus-one problem

witness #999

N
1,901
|A|
24
exponent log |A| / log N
0.4209
status
current record for this modulus
submitted by
David Renshaw
submitted at
2026-08-05 11:40:50 UTC

Elements (24)

60, 102, 120, 162, 210, 252, 450, 492, 540, 582, 600, 642, 1167, 1227, 1233, 1263, 1383, 1557, 1647, 1653, 1707, 1773, 1797, 1803

Commentary

Improves witness#149 from size 23 to 24. Derived from witness#151 (N = 1945, size 29): apply the affine automorphism x -> 1939x + 1158 (mod 1945), reinterpret the resulting residues modulo 1901, then greedily hit all 107 resulting distinct conflict supports. This was transform 772 of transfer-search seed 5805. A second independent affine transfer also produced size 24; a subsequent sweep of 738,870 transfers found no size-25 subset. Independently checked before submission by literal enumeration of all 24^4 = 331,776 ordered quadruples: exactly 24 solutions, all diagonal.

last edited by David Renshaw at 2026-08-05 11:41:06 UTC · history

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