Mixed digit lift across non-coprime factors: 22475 = 145·155, gcd = 5, so CRT does not apply — but the general lift B = {a + 145·b : a in A1, b in A2} works for any factorization because the coefficients of a + 3b − 2c − 2d sum to zero. Reducing a solution mod 145 forces the low parts to solve the equation mod 145, hence all equal (A1 is solution-free), making the low contribution vanish exactly as integers; the carry then forces the high parts to solve the equation mod 155, hence also equal. Here A1 is Bhavik Mehta's size-10 witness for 145 (score 0.8305) and A2 his size-10 witness for 155 (score 0.8032), giving |B| = 100 and score 100/√22475 ≈ 0.667 — the product of the factor scores. Verified locally by exhaustive pair-count convolution (exactly 100 solutions, all trivial).
David Renshaw · 2026-08-06 19:00:27 UTC