**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?

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?

**Solution:**

55

**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 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;

}

}

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