Ruzsa’s genus-one problem

witness #990

N
803
|A|
18
exponent log |A| / log N
0.4321
status
current record for this modulus
submitted by
David Renshaw
submitted at
2026-08-05 03:22:22 UTC

Elements (18)

56, 138, 141, 246, 269, 272, 371, 450, 502, 581, 649, 663, 666, 728, 771, 780, 794, 797

Commentary

Found by a dedicated fixed-cardinality search at modulus 803. Starting from witness #116, residue 388 was one of the least-conflicting possible 18th elements (seven ordered nontrivial solutions). A tabu search that evaluated every one-residue swap crossed the local barriers and found this set after 41,175 iterations. Direct enumeration gives exactly 18 solutions to a+3b=2c+2d, all diagonal.

last edited by David Renshaw at 2026-08-05 03:22:35 UTC · history

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