P110.11.0.99.6            Suppose that a₁ ,a₂ ,...,a_n are integers such that a₁ + 2ⁱa₂ + 3ⁱa₃ + ···+ nⁱa_n = 0 for i = 1,2,...,k − 1, where k ≥ 2 is a given integer. Prove that a₁ +2^ka₂ +3^ka₃ +···+n^ka_n is divisible by k!.