2018-09-30 22:01:58 +00:00
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---
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id: 5900f4651000cf542c50ff77
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title: 'Problem 248: Numbers for which Euler’s totient function equals 13!'
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2020-11-27 18:02:05 +00:00
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challengeType: 5
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2019-08-05 16:17:33 +00:00
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forumTopicId: 301895
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2021-01-13 02:31:00 +00:00
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dashedName: problem-248-numbers-for-which-eulers-totient-function-equals-13
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2018-09-30 22:01:58 +00:00
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---
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2020-11-27 18:02:05 +00:00
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# --description--
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2018-09-30 22:01:58 +00:00
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2021-07-16 10:21:45 +00:00
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The first number $n$ for which $φ(n) = 13!$ is $6\\,227\\,180\\,929$.
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2018-09-30 22:01:58 +00:00
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2021-07-16 10:21:45 +00:00
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Find the ${150\\,000}^{\text{th}}$ such number.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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# --hints--
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2018-09-30 22:01:58 +00:00
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2021-07-16 10:21:45 +00:00
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`eulersTotientFunctionEquals()` should return `23507044290`.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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```js
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2021-07-16 10:21:45 +00:00
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assert.strictEqual(eulersTotientFunctionEquals(), 23507044290);
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2018-09-30 22:01:58 +00:00
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```
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2020-11-27 18:02:05 +00:00
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# --seed--
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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## --seed-contents--
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2018-09-30 22:01:58 +00:00
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```js
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2021-07-16 10:21:45 +00:00
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function eulersTotientFunctionEquals() {
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2020-09-15 16:57:40 +00:00
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2018-09-30 22:01:58 +00:00
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return true;
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}
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2021-07-16 10:21:45 +00:00
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eulersTotientFunctionEquals();
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2018-09-30 22:01:58 +00:00
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```
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2020-11-27 18:02:05 +00:00
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# --solutions--
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2018-09-30 22:01:58 +00:00
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```js
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// solution required
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```
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