Let A, B, C, D, E be integers in {0, 1, 2, . . . , 9}, and consider the five-digit numbers n = ABCDE and m = EABCD (written in the standard decimal form).
a) Show that if m is divisible by 9, then n is also divisible by 9. (1p)
b) Show that if m is divisible by 271, then n is also divisible by 271. (3p)