freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-66-diophantine-equation.english.md

---
id: 5900f3ae1000cf542c50fec1
challengeType: 5
title: 'Problem 66: Diophantine equation'
---

## Description
<section id='description'>
Consider quadratic Diophantine equations of the form:
x2 – Dy2 = 1
For example, when D=13, the minimal solution in x is 6492 – 13×1802 = 1.
It can be assumed that there are no solutions in positive integers when D is square.
By finding minimal solutions in x for D = {2, 3, 5, 6, 7}, we obtain the following:
32 – 2×22 = 1
22 – 3×12 = 192 – 5×42 = 1
52 – 6×22 = 1
82 – 7×32 = 1
Hence, by considering minimal solutions in x for D ≤ 7, the largest x is obtained when D=5.
Find the value of D ≤ 1000 in minimal solutions of x for which the largest value of x is obtained.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler66()</code> should return 661.
    testString: assert.strictEqual(euler66(), 661, '<code>euler66()</code> should return 661.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler66() {
  // Good luck!
  return true;
}

euler66();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>