As dan-robertson mentioned in another branch, you don't even need induction - you can sidestep it by writing X = sum_i x_i 10^i and noticing that all the 10^i a

As dan-robertson mentioned in another branch, you don't even need induction - you can sidestep it by writing X = sum_i x_i 10^i and noticing that all the 10^i are 1 modulo 9 (and therefore modulo 3).