Project Euler > Problem 110 > Diophantine reciprocals II (Java Solution)

Problem:

In the following equation x, y, and n are positive integers.

1

x
+
1

y
=
1

n

It can be verified that when n = 1260 there are 113 distinct solutions and this is the least value of n for which the total number of distinct solutions exceeds one hundred.

What is the least value of n for which the number of distinct solutions exceeds four million?

NOTE: This problem is a much more difficult version of problem 108 and as it is well beyond the limitations of a brute force approach it requires a clever implementation.

Solution:

142913828922

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

public interface EulerSolution{

public String run();

}

/* 
 * Solution to Project Euler problem 10
 * By Nayuki Minase
 * 
 * http://nayuki.eigenstate.org/page/project-euler-solutions
 * https://github.com/nayuki/Project-Euler-solutions
 */


public final class p010 implements EulerSolution {
	
	public static void main(String[] args) {
		System.out.println(new p010().run());
	}
	
	
	private static final int LIMIT = 2000000;
	
	public String run() {
		long sum = 0;
		for (int p : Library.listPrimes(LIMIT - 1))
			sum += p;
		return Long.toString(sum);
	}
	
}