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题目：
Description
Given an integer n, find out number of ways to represent it as the sum of two or more integers ai with the next property: ratio ai / ai - 1is the same positive integer for all possible i > 1.
Input
Input consists of one integer n (1 ≤ n ≤ 105).
Output
Print one integer — number of representations.
Sample Input
1
0
5
2
567
21
Hint
In the first sample no such representation exists.
In the second sample there exist two representations:
题目大意：给出一个等比数列（至少连个元素）的和n，要求公比q为整数，求满足要求的等比数列的个数。
题目思路：Sn=a1*(1-q^n)/(1-q),枚举q的值，判断a1是否为整数，比较暴力……
1 #include<iostream> 2 #include<algorithm> 3 #include<cstring> 4 #include<vector> 5 #include<stdio.h> 6 #include<stdlib.h> 7 #include<queue> 8 #include<math.h> 9 #define INF 0x3f3f3f3f 10 #define MAX 1000005 11 #define Temp 1000000000 12 13 using namespace std; 14 15 int check(long long q,long long n) 16 { 17 long long a=q; 18 int ans=0; 19 while(n*(q-1)/(a-1) >= 1) 20 { 21 if(n*(q-1)%(a-1)==0 && n*(q-1)/(a-1)>=1 && n*(q-1)/(a-1)<n)//判断a1是否为整数，且满足要求 22 ans++; 23 a*=q; 24 } 25 return ans; 26 } 27 28 int main() 29 { 30 int n,sum; 31 sum=0; 32 scanf("%d",&n); 33 for(int i=1; i<n; i++) 34 { 35 if(n%i==0 && n/i>1) 36 sum++; 37 } 38 for(int i=2; i<n; i++)//枚举公比的值 39 { 40 sum+=check(i,n); 41 } 42 printf("%d\n",sum); 43 return 0; 44 }
Gym 100917C Constant Ratio 数论+暴力
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原文地址：http://www.cnblogs.com/alan-W/p/5927483.html
