求助prep上一道数学题

logowuyi

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)=
p-1    p-2   (p+1)/2   (p-1)/2    2

答案是第一个，不太明白~~后天就考试了，数学还这样，着急啊~~

bettyofariN

第一道我也迷惑的，虽然想法不精确，还是说一下。比如f(3)=2,1。 f(5)=4,3,2,1。f(7)=6,5,4,3,2,1。能看出来是p-1。原因应该是既然n为质数，那么n-1到1都满足条件。所以是p-1个。容易误区的是判断是否满足条件时会不自觉限定成质数（我就是这样的）。
如果不对的话，请大家指正。

logowuyi

还有一道题
If n is a positive integer and r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r ?
(1)    2 is not a factor of n
(2)    3 is not a factor of n
答案是C   这道题也很不明白啊~~