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50 lines
1.0 KiB
Markdown
50 lines
1.0 KiB
Markdown
---
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id: 5900f5331000cf542c510046
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title: 'Problem 455: Powers With Trailing Digits'
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challengeType: 1
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forumTopicId: 302129
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dashedName: problem-455-powers-with-trailing-digits
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---
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# --description--
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Let $f(n)$ be the largest positive integer $x$ less than ${10}^9$ such that the last 9 digits of $n^x$ form the number $x$ (including leading zeros), or zero if no such integer exists.
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For example:
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$$\begin{align}
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& f(4) = 411\\,728\\,896 (4^{411\\,728\\,896} = ...490\underline{411728896}) \\\\
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& f(10) = 0 \\\\
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& f(157) = 743\\,757 (157^{743\\,757} = ...567\underline{000743757}) \\\\
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& Σf(n), 2 ≤ n ≤ 103 = 442\\,530\\,011\\,399
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\end{align}$$
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Find $\sum f(n)$, $2 ≤ n ≤ {10}^6$.
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# --hints--
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`powersWithTrailingDigits()` should return `450186511399999`.
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```js
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assert.strictEqual(powersWithTrailingDigits(), 450186511399999);
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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 powersWithTrailingDigits() {
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return true;
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}
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powersWithTrailingDigits();
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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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