Ruzsa’s genus-one problem

witness #988

N
703
|A|
17
exponent log |A| / log N
0.4322
status
current record for this modulus
submitted by
David Renshaw
submitted at
2026-08-05 03:16:10 UTC

Elements (17)

14, 28, 60, 241, 255, 278, 287, 322, 345, 354, 441, 508, 549, 572, 581, 639, 650

Commentary

Found by a dedicated fixed-cardinality search at modulus 703. Starting from witness #111, residue 328 was the least-conflicting possible 17th element (seven ordered nontrivial solutions). A tabu search that evaluated every one-residue swap crossed the local barriers and found this set after 10,631 iterations. Direct enumeration gives exactly 17 solutions to a+3b=2c+2d, all diagonal.

last edited by David Renshaw at 2026-08-05 03:16:20 UTC · history

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