[HDOJ1492]Happy 2004（数论，快速幂，逆元，积性函数）

Posted 2020-08-06

题目链接：http://acm.split.hdu.edu.cn/showproblem.php?pid=1452

题意：求2004^n的所有因子和。

 1 #include <algorithm>
 2 #include <iostream>
 3 #include <iomanip>
 4 #include <cstring>
 5 #include <climits>
 6 #include <complex>
 7 #include <fstream>
 8 #include <cassert>
 9 #include <cstdio>
10 #include <bitset>
11 #include <vector>
12 #include <deque>
13 #include <queue>
14 #include <stack>
15 #include <ctime>
16 #include <set>
17 #include <map>
18 #include <cmath>
19 using namespace std;
20 #define fr first
21 #define sc second
22 #define cl clear
23 #define BUG puts("here!!!")
24 #define W(a) while(a--)
25 #define pb(a) push_back(a)
26 #define Rint(a) scanf("%d", &a)
27 #define Rll(a) scanf("%I64d", &a)
28 #define Rs(a) scanf("%s", a)
29 #define Cin(a) cin >> a
30 #define FRead() freopen("in", "r", stdin)
31 #define FWrite() freopen("out", "w", stdout)
32 #define Rep(i, len) for(int i = 0; i < (len); i++)
33 #define For(i, a, len) for(int i = (a); i < (len); i++)
34 #define Cls(a) memset((a), 0, sizeof(a))
35 #define Clr(a, x) memset((a), (x), sizeof(a))
36 #define Full(a) memset((a), 0x7f7f7f, sizeof(a))
37 #define lrt rt << 1
38 #define rrt rt << 1 | 1
39 #define pi 3.14159265359
40 #define RT return
41 #define lowbit(x) x & (-x)
42 #define onecnt(x) __builtin_popcount(x)
43 typedef long long LL;
44 typedef long double LD;
45 typedef unsigned long long ULL;
46 typedef pair<int, int> pii;
47 typedef pair<string, int> psi;
48 typedef pair<int, int> pll;
49 typedef map<string, int> msi;
50 typedef vector<int> vi;
51 typedef vector<int> vl;
52 typedef vector<vl> vvl;
53 typedef vector<bool> vb;
54 
55 const LL mod = 29;
56 LL n;
57 
58 LL mul(LL x, LL q) {
59     LL ret = 1;
60     while(q) {
61         if(q & 1) ret = (ret * x) % mod;
62         q >>= 1;
63         x = (x * x) % mod;
64     }
65     return ret;
66 }
67 
68 LL exgcd(LL a, LL b, LL &x, LL &y) {
69     if(b == 0) {
70         x = 1;
71         y = 0;
72         return a;
73     }
74     else {
75         LL ret = exgcd(b, a%b, x, y);
76         LL tmp = x;
77         x = y;
78         y = tmp - a / b * y;
79         return ret;
80     }
81 }
82 
83 LL iv(LL a) {
84     LL x, y;
85     exgcd(a, mod, x, y);
86     return (x % mod + mod) % mod;
87 }
88 
89 signed main() {
90     // FRead();
91     while(cin >> n && n) {
92         cout << ((mul(2, 2*n+1)-1)%mod)*((mul(3, n+1)-1)*iv(2)%mod)*((mul(167,n+1)-1)*iv(166)%mod)%mod << endl;
93     }
94     RT 0;
95 }