1af6e7aa5a
* fix: clean-up Project Euler 321-340 * fix: typo * fix: corrections from review Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
51 lines
1011 B
Markdown
51 lines
1011 B
Markdown
---
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id: 5900f4b21000cf542c50ffc5
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title: 'Problem 326: Modulo Summations'
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challengeType: 5
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forumTopicId: 301983
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dashedName: problem-326-modulo-summations
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---
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# --description--
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Let an be a sequence recursively defined by: $a_1 = 1$, $\displaystyle a_n = \left(\sum_{k = 1}^{n - 1} k \times a_k\right)\bmod n$.
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So the first 10 elements of $a_n$ are: 1, 1, 0, 3, 0, 3, 5, 4, 1, 9.
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Let $f(N, M)$ represent the number of pairs $(p, q)$ such that:
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$$ 1 \le p \le q \le N \\; \text{and} \\; \left(\sum_{i = p}^q a_i\right)\bmod M = 0$$
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It can be seen that $f(10, 10) = 4$ with the pairs (3,3), (5,5), (7,9) and (9,10).
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You are also given that $f({10}^4, {10}^3) = 97\\,158$.
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Find $f({10}^{12}, {10}^6)$.
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# --hints--
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`moduloSummations()` should return `1966666166408794400`.
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```js
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assert.strictEqual(moduloSummations(), 1966666166408794400);
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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 moduloSummations() {
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return true;
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}
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moduloSummations();
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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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