IMO 1975

For students of class 6-8 (age 12 to 14)
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IMO 1975

Unread post by umme.habiba.lamia » Mon Dec 04, 2017 1:04 pm

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.

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