The answer to exercise marked [BB] can be found in the Back of the Book.
(a) [BB] Let x be an integer expressed in base 10. Suppose the sum of the digits of x is divisible by 3. Prove that xis divisible by 3.
(b) [BB] Prove that if an integer x is divisible by 3 then, when written in base 10, the sum of the digits of xis divisible by 3.
(c) Repeat (a) and (b) for the integer 9.
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