hdu 5597GTW likes function(欧拉函数)

题目链接：【hdu 5597】

f(n)=sum((-1)^k * 2^(2n-2k) * C(k, 2n-k+1)) 0<=k<=n

这个公式化简之后就是f(x) = x+1

简单证明一下

首先要知道C(m,n)+C(m+1, n) = C(m+1, n+1)

<span style="font-size:14px;">#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <string>
using namespace std;
#define ll __int64
int main()
{ll n, x;while(~scanf("%I64d%I64d", &n, &x)){x = n+x+1;ll ans=x;for(ll i=2; i*i<=x; i++){if(x%i==0) {ans=ans/i*(i-1);while(x%i==0) x/=i;}}if(x>1) ans=ans/x*(x-1);printf("%I64d\n", ans);}return 0;
}</span>

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