45 lines
727 B
Markdown
45 lines
727 B
Markdown
---
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id: 5900f5041000cf542c510016
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title: 'Problem 407: Idempotents'
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challengeType: 5
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forumTopicId: 302075
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dashedName: problem-407-idempotents
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---
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# --description--
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If we calculate $a^2\bmod 6$ for $0 ≤ a ≤ 5$ we get: 0, 1, 4, 3, 4, 1.
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The largest value of a such that $a^2 ≡ a\bmod 6$ is $4$.
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Let's call $M(n)$ the largest value of $a < n$ such that $a^2 ≡ a (\text{mod } n)$. So $M(6) = 4$.
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Find $\sum M(n)$ for $1 ≤ n ≤ {10}^7$.
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# --hints--
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`idempotents()` should return `39782849136421`.
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```js
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assert.strictEqual(idempotents(), 39782849136421);
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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 idempotents() {
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return true;
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}
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idempotents();
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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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