79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
68 lines
1.5 KiB
Markdown
68 lines
1.5 KiB
Markdown
---
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id: 5900f5131000cf542c510025
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challengeType: 5
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title: 'Problem 422: Sequence of points on a hyperbola'
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---
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## Description
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<section id='description'>
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Let H be the hyperbola defined by the equation 12x2 + 7xy - 12y2 = 625.
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Next, define X as the point (7, 1). It can be seen that X is in H.
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Now we define a sequence of points in H, {Pi : i ≥ 1}, as:
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P1 = (13, 61/4).
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P2 = (-43/6, -4).
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For i > 2, Pi is the unique point in H that is different from Pi-1 and such that line PiPi-1 is parallel to line Pi-2X. It can be shown that Pi is well-defined, and that its coordinates are always rational.
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You are given that P3 = (-19/2, -229/24), P4 = (1267/144, -37/12) and P7 = (17194218091/143327232, 274748766781/1719926784).
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Find Pn for n = 1114 in the following format:If Pn = (a/b, c/d) where the fractions are in lowest terms and the denominators are positive, then the answer is (a + b + c + d) mod 1 000 000 007.
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For n = 7, the answer would have been: 806236837.
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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>euler422()</code> should return 92060460.
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testString: assert.strictEqual(euler422(), 92060460, '<code>euler422()</code> should return 92060460.');
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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 euler422() {
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// Good luck!
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return true;
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}
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euler422();
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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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