求一道数学题意和题解

joanjoans

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 than f(p)=

A. p-1

B. p-2

C. (p+1)/2

D. (p-1)/2

E. 2

正确答案是A.

请高人指点下,这道题意是什么?怎么解呢? 多谢拉!

xp635

我的理解：

f(n)=小于n的正整数,但是这些正整数不包括于n相差1的因素

如果p为质数，因素只有1和p本身,

所以f(p)=p-1

jjapolloer

任何一个质数和小于此质数的正整数除了公因子1外，没有其他公因子，所以f(p)的个数就是小于p的所有正整数，即p-1.

joanjoans

 谢谢你!!!!