(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.
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Expert's answer
2020-12-08T10:12:25-0500
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"
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