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.

## IMO 1975

- samiul_samin
**Posts:**1007**Joined:**Sat Dec 09, 2017 1:32 pm

### Re: IMO 1975

($C$)You can get the solution here

- samiul_samin
**Posts:**1007**Joined:**Sat Dec 09, 2017 1:32 pm

### Re: IMO 1975

Problems are from The art and craft of problem solving book.umme.habiba.lamia wrote: ↑Mon Dec 04, 2017 1:04 pmLet $f(n)$ 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.