Multiples of three P61930

A well-kown mathematical property states that a natural number is a multiple of three if and only if the sum of its digits is also a multiple of three. For instance, the sum of the digits of 8472 is $8 + 4 + 7 + 2 = 21$, which is a multiple of three. Therefore, 8472 is also a multiple of three.

Implement a recursive function that tells if a strictly positive natural number @n@ is a multiple of three or not.

    bool is_multiple_3(int n);

Interface

bool is_multiple_3(int n);

int is_multiple_3(int n);

public static boolean isMultiple3(int n);

is_multiple_3(n)  # returns bool

is_multiple_3(n: int) -> bool

Solve this problem using a recursive function to return the sum of the digits of a natural number @n@.

    int sum_of_digits(int n);

Interface

int sum_of_digits(int n);

int sum_of_digits(int n);

public static int sumOfDigits(int n);

sum_of_digits(n)  # returns int

sum_of_digits(n: int) -> int

Observation

Here, you are allowed to use the operations of division and integer remainder only with the number 10. Otherwise, this exercise would be totally trivial!