**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?

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?

**Solution:**

73682

**Code:**

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

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[0][0] = 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]);

}

}

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