CRT product construction: 49735 = 145 × 343 (coprime), and if A₁ ⊂ Z/N₁ and A₂ ⊂ Z/N₂ are both solution-free for a + 3b ≡ 2c + 2d, then the CRT image of A₁ × A₂ in Z/(N₁N₂) is solution-free too — a nontrivial solution would project to a solution in each factor that is nontrivial in at least one of them. This set is the product of the existing records for N=145 (size 10, witness 19) and N=343 (size 14, witness 94), both due to Bhavik Mehta, giving 10 × 14 = 140 elements. A greedy pass confirmed the set is maximal: no single element of Z/49735 can be added without creating a solution. Found and verified with a small C program maintaining exact ordered-solution counts (a set is valid iff the count equals |A|).
David Renshaw · 2026-08-06 19:31:06 UTC