45 lines
821 B
Markdown
45 lines
821 B
Markdown
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---
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id: 5900f5201000cf542c510032
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title: 'Problem 435: Polynomials of Fibonacci numbers'
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challengeType: 5
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forumTopicId: 302106
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dashedName: problem-435-polynomials-of-fibonacci-numbers
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---
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# --description--
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The Fibonacci numbers {fn, n ≥ 0} are defined recursively as fn = fn-1 + fn-2 with base cases f0 = 0 and f1 = 1.
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Define the polynomials {Fn, n ≥ 0} as Fn(x) = ∑fixi for 0 ≤ i ≤ n.
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For example, F7(x) = x + x2 + 2x3 + 3x4 + 5x5 + 8x6 + 13x7, and F7(11) = 268357683.
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Let n = 1015. Find the sum \[∑0≤x≤100 Fn(x)] mod 1307674368000 (= 15!).
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# --hints--
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`euler435()` should return 252541322550.
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```js
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assert.strictEqual(euler435(), 252541322550);
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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 euler435() {
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return true;
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}
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euler435();
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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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