Week 5: Wednesday
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Q1. (50)

The mth Bernoulli number B(m) is defined recursively as follows:

B(m) = 1 - sum of all (k = 0 to m - 1) of { (m choose k) * B(k) / (m - k + 1) }

The base case is B(0) = 1.

Write a program to compute the first 10 Bernoulli numbers.

Q2. (50)

The totient number T(n) of a positive integer n is defined to be the number of
positive integers less than or equal to n that are coprime to n (i.e., having
no common factor other than 1).

For example, T(1) = 1 (special case); T(9) = 6 (as 1, 2, 4, 5, 7 and 8 are
coprime with 9).

Write a program that takes a positive integer as input and calculates its
totient number. Your program should implement the following two functions
(other than the main): 
	1. int coprime(int m, int n): returns 1 if m and n are co-prime, 0 otherwise
	2. int totient(int n): returns the totient number of n