## Problem:

There are some prime values, p, for which there exists a positive integer, n, such that the expression n3 + n2p is a perfect cube.

For example, when p = 19, 83 + 82[×]19 = 123.

What is perhaps most surprising is that for each prime with this property the value of n is unique, and there are only four such primes below one-hundred.

How many primes below one million have this remarkable property?

73682

## Code:The solution may include methods that will be found here: Library.java .

public interface EulerSolution{public String run();}
/*  * Solution to Project Euler problem 31 * By Nayuki Minase *  * http://nayuki.eigenstate.org/page/project-euler-solutions * https://github.com/nayuki/Project-Euler-solutions */public final class p031 implements EulerSolution {		public static void main(String[] args) {		System.out.println(new p031().run());	}			private static final int TOTAL = 200;	private static int[] COINS = {1, 2, 5, 10, 20, 50, 100, 200};		public String run() {		// Knapsack problem. ways[i][j] is the number of ways to use		// any of the first i coin values to form an unordered sum of j.		int[][] ways = new int[COINS.length + 1][TOTAL + 1];		ways = 1;		for (int i = 0; i < COINS.length; i++) {			for (int j = 0; j <= TOTAL; j++)				ways[i + 1][j] = ways[i][j] + (j >= COINS[i] ? ways[i + 1][j - COINS[i]] : 0);  // Dynamic programming		}		return Integer.toString(ways[COINS.length][TOTAL]);	}	}