Question

For distinct prime numbers p and q, Euler's totient function phi(pq) is equal to:

a) pq
b) (p+1)(q+1)
c) (p-1)(q-1)
d) p + q

Answer 1

Euler's totient function φ(pq) for distinct prime numbers p and q is given by (p-1)(q-1), since all positive integers less than pq are relatively prime to pq except for the multiples of p and q.

Step-by-step explanation:

The question is asking for the value of Euler's totient function φ(pq) for distinct prime numbers p and q. Euler's totient function, denoted φ(n), is the number of positive integers up to n that are relatively prime to n. For two distinct prime numbers p and q, the totient of their product pq is given by φ(pq) = (p-1)(q-1), as p and q have no common divisors other than 1, and so all numbers less than pq except for the multiples of p and q are relatively prime to pq.

Therefore, the answer to the question for φ(pq) is c) (p-1)(q-1).