A = B ⊕ 85·{0,1} where B is the parabola in the group (ℤ/85)², placed in ℤ/44455 = ℤ/(85·523) by CRT with the second coordinate confined to a short interval. Since 85 = 5·17 and both 5, 17 ≡ 5 (mod 12), 3 is a quadratic non-residue mod each, so Ruzsa’s identity 3(x_a−x_b)² = 4(x_c−x_d)² forces triviality and B is exactly valid. Composite g gives sparser squares, hence a shorter v-support span, hence a smaller M.
Rayan Hatout · 2026-09-01 09:14:21 UTC