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Description
We say that integer x, 0 < x < p, is a primitive root modulo odd prime p if and only if the set { (xi mod p) | 1 <= i <= p-1 } is equal to { 1, …, p-1 }. For example, the consecutive powers of 3 modulo 7 are 3, 2, 6, 4, 5, 1, and thus 3 is a primitive root modulo 7.
Write a program which given any odd prime 3 <= p < 65536 outputs the number of primitive roots modulo p. InputEach line of the input contains an odd prime numbers p. Input is terminated by the end-of-file seperator.
OutputFor each p, print a single number that gives the number of primitive roots in a single line.
Sample Input23
31 79 Sample Output10
8 24看了会欧拉函数的内容,准备自己独立做一个题目,结果就碰上这种题,想了半天想不出来,百度了才知道还有个定理。。。我果然不适合搞数学
定理:如果p有原根,则它恰有φ(φ(p))个不同的原根,p为素数,当然φ(p)=p-1,因此就有φ(p-1)个原根
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