Problem 48

The series, 1¹ + 2² + 3³ + ... + 10¹⁰ = 10405071317.

Find the last ten digits of the series, 1¹ + 2² + 3³ + ... + 1000¹⁰⁰⁰.

C++:

#include 
     
      using namespace std;typedef unsigned long long ULL;const ULL DIGITS10 = 10000000000;// 模幂函数ULL powermod(__uint128_t a, int n, ULL m){    __uint128_t res = 1L;    while(n) {        if(n & 1L) {            res *= a;            res %= m;        }        a *= a;        a %= m;        n >>= 1;    }    return (ULL)res;}int main(){    long n;    ULL ans;    while(cin >> n) {        ans = 0;        for(int i=1; i<=n; i++) {            ans += powermod(i, i, DIGITS10);            ans %= DIGITS10;        }        cout << ans << endl;    }    return 0;}
     

Python:

print(sum([(x**x)%(10**10) for x in range(1,1001)])%(10**10))