问一道数学PREP

vrtjtrj

题目被关了，不记得具体了，大致是
the function f is defined for all positive n by the following rule, f(n) is the number of positive number each of which is less than n and has no positive in common with n other than 1. If p is any prime number then f(p)=?

the answer is p-1

请问何解？

sdcar2010

Simple. Since p is a prime number, it does not share any common factors with the number from 1 to p-1. Then f(p) = p-1.