请教PREP 37题，看不懂啊。。。

cptbtptp

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)  (p+1)/2
(D)  (p-1)/2
(E) 2


不懂f(n)到底是什么个意思啊
求指教

cptbtptp

米有人理我吗

FIGHTING618

A吗？

cptbtptp

是A， 这个题是什么意思啊

FIGHTING618

这个题就是说F(n)是小于N且没有与N有共同因子（除了1）的数的个数，有点绕。。

cptbtptp

这个题就是说F(n)是小于N且没有与N有共同因子（除了1）的数的个数，有点绕。。

-- by 会员 FIGHTING618 (2011/6/7 22:49:12)

还是不会，请NN解释一下

FIGHTING618

因为P是质数，因此与比它小的所有数都没有除了1以外的公因子。所以选A.

liulujun

Take a prime number and figure out a specific soln for that prime number.
Let p = 5. So, excluding 1, the other numbers that have no factors common with 5 are 1,2,3,4.
Let p = 7. So, excluding 1, the other numbers that have no factors common with 7 are,1,2,3,4,5,6
Do you see the pattern? For any prime number, all the numbers less than it will have no factors in common with it except 1.
So f(p) = p - 1
Answer is A

camelo777

我还是没懂，那p-2怎么错了？ P=7的话，减去2是5，不也没有相同的因子吗？

MarsTOF

我还是没懂，那p-2怎么错了？ P=7的话，减去2是5，不也没有相同的因子吗？

-- by 会员 camelo777 (2011/6/8 8:07:39)