**Problem:**

The positive integers, x, y, and z, are consecutive terms of an arithmetic progression. Given that n is a positive integer, the equation, x2 [−] y2 [−] z2 = n, has exactly one solution when n = 20:

132 [−] 102 [−] 72 = 20

In fact there are twenty-five values of n below one hundred for which the equation has a unique solution.

How many values of n less than fifty million have exactly one solution?

132 [−] 102 [−] 72 = 20

In fact there are twenty-five values of n below one hundred for which the equation has a unique solution.

How many values of n less than fifty million have exactly one solution?

**Solution:**

872187

**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 36

* By Nayuki Minase

*

* http://nayuki.eigenstate.org/page/project-euler-solutions

* https://github.com/nayuki/Project-Euler-solutions

*/

public final class p036 implements EulerSolution {

public static void main(String[] args) {

System.out.println(new p036().run());

}

public String run() {

int sum = 0;

for (int i = 1; i < 1000000; i++) {

if (Library.isPalindrome(Integer.toString(i, 10)) && Library.isPalindrome(Integer.toString(i, 2)))

sum += i;

}

return Integer.toString(sum);

}

}

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