Codeforces Round #372 (Div. 2) C. Plus and Square Root

题目链接

分析：这题都过了2000了，应该很简单。。写这篇只是为了凑篇数= =

假设在第i级的时候开方过后的数为i∗t[i]，t[i]是第i级的系数。那么

(3t[3])2−(2t[2])≡0(mod2)

(4t[4])2−(3t[3])≡0(mod3)

(5t[5])2−(4t[4])≡0(mod4)

…

(3t[3])2≡0(mod2)

(4t[4])2≡0(mod3)

(5t[5])2≡0(mod4)

显然，最小的情况应该就是t[i]=i−1, 化简一下公式，在i的情况下应该是i∗i∗(i−1)−(i−2)，注意i=2时特殊情况，应该为2。

/*****************************************************/
//#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <map>
#include <set>
#include <ctime>
#include <stack>
#include <queue>
#include <cmath>
#include <string>
#include <vector>
#include <cstdio>
#include <cctype>
#include <cstring>
#include <sstream>
#include <cstdlib>
#include <iostream>
#include <algorithm>
using namespace std;
#define   offcin        ios::sync_with_stdio(false)
#define   sigma_size    26
#define   lson          l,m,v<<1
#define   rson          m+1,r,v<<1|1
#define   slch          v<<1
#define   srch          v<<1|1
#define   sgetmid       int m = (l+r)>>1
#define   LL            long long
#define   ull           unsigned long long
#define   mem(x,v)      memset(x,v,sizeof(x))
#define   lowbit(x)     (x&-x)
#define   bits(a)       __builtin_popcount(a)
#define   mk            make_pair
#define   pb            push_back
#define   fi            first
#define   se            second

const int    INF    = 0x3f3f3f3f;
const LL     INFF   = 1e18;
const double pi     = acos(-1.0);
const double inf    = 1e18;
const double eps    = 1e-9;
const LL     mod    = 1e9+7;
const int    maxmat = 10;
const ull    BASE   = 31;

/*****************************************************/

int main(int argc, char const *argv[]) {
    int N;
    cin>>N;
    for (int i = 2; i <= N + 1; i ++) {
        if (i == 2) puts("2");
        else printf("%I64d\n", 1LL * i * i * (i -1) - 1LL * (i - 2));
    }
    return 0;
}