A cubic number is the result of using a whole number in a multiplication three times. For example, 3×3×3=27so
is a cubic number. The first few cubic numbers are 1,8,27,64 and 125. Given an prime number p. Check that if
is a difference of two cubic numbers.
InputThe first of input contains an integer T (1≤T≤100) which is the total number of test cases.
For each test case, a line contains a prime number p (2≤p≤10^12).OutputFor each test case, output 'YES' if given p
is a difference of two cubic numbers, or 'NO' if not.
Sample Input
10 2 3 5 7 11 13 17 19 23 29
Sample Output
NO NO NO YES NO NO NO YES NO NO
题意:给一个质数,判断该质数是否为两立方数之差
首先x^3-y^3为一个质数则展开立方差公式后发现:x=y+1
带入化简,得3*y(y+1)+1
所以一个质数n要是两立方数之差。有n-1是3的倍数,且n-1是两相邻数之积
#include<iostream> #include <climits> #include <cstdio> #include <algorithm> #define LL long long using namespace std; int main() { int T; scanf("%d", &T); while (T--) { LL n; scanf("%lld", &n); //P=3*(y+1)*y+1 if ((n - 1) % 3) { printf("NO\n"); continue; } LL x = (LL)sqrt((n - 1) / 3); if (x*(x + 1) == (n - 1) / 3) printf("YES\n"); else printf("NO\n"); } return 0; }