(a) Obtain the following generalization of Theorem 4.6: If the integer N is represented in...

(a) Obtain the following generalization of Theorem 4.6: If the integer N is represented in the base b by

then b − 1 | N if and only if b − 1 | (am + ⋯ + a2 + a1 + a0).

(b) Give criteria for the divisibility of N by 3 and 8 that depend on the digits of N when written in the base 9.

(c) Is the integer (447836)9 divisible by 3 and 8?