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---
id: 5900f5331000cf542c510046
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title: 'Problema 455: Potências com algarismos à direita'
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challengeType: 5
forumTopicId: 302129
dashedName: problem-455-powers-with-trailing-digits
---
# --description--
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Considere $f(n)$ como o maior número inteiro positivo $x$ inferior a ${10}^9$, tal que os últimos 9 algarismos de $n^x$ formam o número $x$ (incluindo zeros à esquerda) ou zero, se nenhum número inteiro desse tipo existir.
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Por exemplo:
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$$\begin{align} & f(4) = 411.728.896 (4^{411.728.896} = ...490\underline{411728896}) \\\\
& f(10) = 0 \\\\ & f(157) = 743.757 (157^{743.757} = ...567\underline{000743757}) \\\\
& Σf(n), 2 ≤ n ≤ 103 = 442.530.011.399 \end{align}$$
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Encontre $\sum f(n)$, $2 ≤ n ≤ {10}^6$.
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# --hints--
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`powersWithTrailingDigits()` deve retornar `450186511399999` .
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```js
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assert.strictEqual(powersWithTrailingDigits(), 450186511399999);
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```
# --seed--
## --seed-contents--
```js
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function powersWithTrailingDigits() {
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return true;
}
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powersWithTrailingDigits();
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```
# --solutions--
```js
// solution required
```