**Problem:**

Let x be a real number.

A best approximation to x for the denominator bound d is a rational number r/s in reduced form, with s [≤] d, such that any rational number which is closer to x than r/s has a denominator larger than d:

|p/q-x| [<] |r/s-x| [⇒] q [>] d

For example, the best approximation to [√]13 for the denominator bound 20 is 18/5 and the best approximation to [√]13 for the denominator bound 30 is 101/28.

Find the sum of all denominators of the best approximations to [√]n for the denominator bound 1012, where n is not a perfect square and 1 [<] n [≤] 100000.

A best approximation to x for the denominator bound d is a rational number r/s in reduced form, with s [≤] d, such that any rational number which is closer to x than r/s has a denominator larger than d:

|p/q-x| [<] |r/s-x| [⇒] q [>] d

For example, the best approximation to [√]13 for the denominator bound 20 is 18/5 and the best approximation to [√]13 for the denominator bound 30 is 101/28.

Find the sum of all denominators of the best approximations to [√]n for the denominator bound 1012, where n is not a perfect square and 1 [<] n [≤] 100000.

**Solution:**

162

**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();

}

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