Let f(n) denote the sum of the digits of n.

(a) For any integer n, prove that eventually the se quence f(n),f(f(n) ),f(f(f(n))), . . . will become constant. This constant value is called the digital sum of n.

(b) Prove that the digital sum of the product of any two twin primes, other than 3 and 5, is 8. (Twin primes are primes that are consecutive odd numbers, such as 17 and 19.)

(c) (IMO 1975) Let N = 4444^4444. Find f(f(f(n))), without a calculator.