## Problem:

Given the positive integers, x, y, and z, are consecutive terms of an arithmetic progression, the least value of the positive integer, n, for which the equation, x2 [−] y2 [−] z2 = n, has exactly two solutions is n = 27:

342 [−] 272 [−] 202 = 122 [−] 92 [−] 62 = 27

It turns out that n = 1155 is the least value which has exactly ten solutions.

How many values of n less than one million have exactly ten distinct solutions?

55

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

public interface EulerSolution{public String run();}
/*  * Solution to Project Euler problem 35 * By Nayuki Minase *  * http://nayuki.eigenstate.org/page/project-euler-solutions * https://github.com/nayuki/Project-Euler-solutions */public final class p035 implements EulerSolution {		public static void main(String[] args) {		System.out.println(new p035().run());	}			private static final int LIMIT = Library.pow(10, 6);		private boolean[] isPrime = Library.listPrimality(LIMIT - 1);			public String run() {		int count = 0;		for (int i = 0; i < isPrime.length; i++) {			if (isCircularPrime(i))				count++;		}		return Integer.toString(count);	}			private boolean isCircularPrime(int n) {		String s = Integer.toString(n);		for (int i = 0; i < s.length(); i++) {			if (!isPrime[Integer.parseInt(s.substring(i) + s.substring(0, i))])				return false;		}		return true;	}	}