ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
65 lines
1.5 KiB
Markdown
65 lines
1.5 KiB
Markdown
---
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id: 5900f3ae1000cf542c50fec1
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title: 'Problem 66: Diophantine equation'
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challengeType: 5
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forumTopicId: 302178
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dashedName: problem-66-diophantine-equation
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---
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# --description--
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Consider quadratic Diophantine equations of the form:
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<div style='text-align: center;'>x<sup>2</sup> – Dy<sup>2</sup> = 1</div>
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For example, when D=13, the minimal solution in x is 649<sup>2</sup> – 13×180<sup>2</sup> = 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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<div style='margin-left: 2em;'>
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3<sup>2</sup> – 2×2<sup>2</sup> = 1<br>
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2<sup>2</sup> – 3×1<sup>2</sup> = 1<br>
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<strong><span style='color: red;'>9</span></strong><sup>2</sup> – 5×4<sup>2</sup> = 1<br>
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5<sup>2</sup> – 6×2<sup>2</sup> = 1<br>
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8<sup>2</sup> – 7×3<sup>2</sup> = 1<br>
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</div>
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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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# --hints--
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`diophantineEquation()` should return a number.
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```js
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assert(typeof diophantineEquation() === 'number');
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```
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`diophantineEquation()` should return 661.
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```js
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assert.strictEqual(diophantineEquation(), 661);
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```
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# --seed--
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## --seed-contents--
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```js
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function diophantineEquation() {
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return true;
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}
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diophantineEquation();
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```
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# --solutions--
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```js
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// solution required
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```
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