Product/lift construction: {a + 145·b : a ∈ A, b ∈ B} where A is the size-10 record for N=145 (witness 19) and B is the size-10 record for N=175 (witness 72), both due to Bhavik Mehta. Since the coefficients of a + 3b − 2c − 2d sum to zero, reducing any solution mod 145 forces the A-components to form a solution mod 145 (hence all equal), after which the relation 145·(b₁+3b₂−2b₃−2b₄) ≡ 0 mod 25375 forces the B-components to form a solution mod 175 (hence all equal). So solution-freeness lifts and sizes multiply: 10·10 = 100 elements mod 25375 = 145·175. Constructed and verified by Claude.
David Renshaw · 2026-08-06 21:29:35 UTC