22afc2a0ca
Co-authored-by: Oliver Eyton-Williams <ojeytonwilliams@gmail.com> Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com> Co-authored-by: Beau Carnes <beaucarnes@gmail.com>
76 lines
1.2 KiB
Markdown
76 lines
1.2 KiB
Markdown
---
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id: 5900f4ff1000cf542c510011
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challengeType: 5
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isHidden: false
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title: 'Problem 402: Integer-valued polynomials'
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forumTopicId: 302070
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---
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## Description
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<section id='description'>
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It can be shown that the polynomial n4 + 4n3 + 2n2 + 5n is a multiple of 6 for every integer n. It can also be shown that 6 is the largest integer satisfying this property.
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Define M(a, b, c) as the maximum m such that n4 + an3 + bn2 + cn is a multiple of m for all integers n. For example, M(4, 2, 5) = 6.
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Also, define S(N) as the sum of M(a, b, c) for all 0 < a, b, c ≤ N.
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We can verify that S(10) = 1972 and S(10000) = 2024258331114.
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Let Fk be the Fibonacci sequence:
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F0 = 0, F1 = 1 and
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Fk = Fk-1 + Fk-2 for k ≥ 2.
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Find the last 9 digits of Σ S(Fk) for 2 ≤ k ≤ 1234567890123.
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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>euler402()</code> should return 356019862.
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testString: assert.strictEqual(euler402(), 356019862);
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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 euler402() {
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// Good luck!
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return true;
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}
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euler402();
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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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