gcd(i, j) = 1, i0 < 0, ≡mod(i * i0, 1, j), 0 ≤ j, 0 ≤ i ⊦ 1 < j ∧ 1 < i, ∃ i0. ≡mod(i * i0, 1, j) ∧ 0 ≤ i0