Question

(a) We say that two positive integers a, b are relatively prime if the greatest common divisor of a and b is 1. Let p, q be distinct positive prime numbers such that n=pq. Calculate the number of positive integers not exceeding n that are relatively prime to n.

Answer 1

As $n= pq$ , co-prime numbers < n are (n-1) numbers, except: p, 2p, 3p, 4p,…(q-1)p and q, 2q, 3q, 4q,...(p-1)q

$Total = (n-1) - (q-1+p - 1) = n - p - q +1 \; numbers$