67 lines
1.2 KiB
Markdown
67 lines
1.2 KiB
Markdown
---
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id: 5900f3ae1000cf542c50fec1
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challengeType: 5
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title: 'Problem 66: Diophantine equation'
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---
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## Description
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<section id='description'>
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Consider quadratic Diophantine equations of the form:
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x2 – Dy2 = 1
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For example, when D=13, the minimal solution in x is 6492 – 13×1802 = 1.
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It can be assumed that there are no solutions in positive integers when D is square.
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By finding minimal solutions in x for D = {2, 3, 5, 6, 7}, we obtain the following:
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32 – 2×22 = 1
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22 – 3×12 = 192 – 5×42 = 1
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52 – 6×22 = 1
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82 – 7×32 = 1
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Hence, by considering minimal solutions in x for D ≤ 7, the largest x is obtained when D=5.
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Find the value of D ≤ 1000 in minimal solutions of x for which the largest value of x is obtained.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler66()</code> should return 661.
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testString: assert.strictEqual(euler66(), 661);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler66() {
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// Good luck!
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return true;
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}
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euler66();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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