The index of small length sequences

Let n ≥ 2 be a fixed integer. Define (x)n to be the unique integer in the range 0 ≤ (x)n < n which is congruent to x modulo n. Given x1,…,xl ∈ ℤ, let ∥(x1,…,xl)∥1 = min{(ux1)n + ⋯ + (uxl)n:u ∈ ℤ, g...