Problem Solving

The function \(F\) is defined for all positive integers \(n\) by the following rule: \(f(n)\) is the number of positive integers each of which is less than \(n,\) and has no positive factor in common with \(n\) other than \(1. \)If \(p\) is any prime number then \(f(p)=\)

A. \(p-1\)

B. \(p-2\)

C. \(\dfrac{p+1}2\)

D. \(\dfrac{p-1}2\)

E. \(2\)

Answer: A

Source: GMAT Paper Tests