K- prime demise - (Simple math)

https://ac.nowcoder.com/acm/contest/3346/K

The meaning of problems: determining a prime number p not a difference between the two cubic numbers.

This question is just to see half past one would have no idea, read the solution to a problem suddenly realized, too long did not touch math or number theory, about the recording process.

1. The difference between the cubic equation: X ^{. 3} - Y ^{. 3}  = (XY) (X ² + Y XY + ² )

2.(x-y)(x² + xy + y²)=p

3. Because p is a prime number, so that xy = 1

4. x = y + 1 obtained simply formulated into the original 3y (y + 1) = p-1

5. To set up the above formula, (p-1)% 3 == 0 && sqrt ((p-1) / 3) * (sqrt ((p-1) / 3) +1) == (p-1 ) / 3

 

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scan=new Scanner(System.in);
        int n;
        n=scan.nextInt();
        long p;
        while(n!=0) {
            n--;
            p=scan.nextLong();
            if((p-1)%3==0) {
                P = (. 1-P) /. 3 ;
                 Long Y = ( Long ) the Math.sqrt (P); // rounded down 
                IF (Y * (Y +. 1) == P)
                    System.out.println("YES");
                else 
                    System.out.println("NO");
                
            }else 
                System.out.println("NO");
        }
    }
}