2018-10-10 18:03:03 -04:00
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---
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id: 5900f3e71000cf542c50fefa
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2021-11-23 11:06:14 -08:00
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title: '问题 123:素数平方余数'
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2018-10-10 18:03:03 -04:00
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challengeType: 5
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2021-02-06 04:42:36 +00:00
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forumTopicId: 301750
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2021-01-13 03:31:00 +01:00
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dashedName: problem-123-prime-square-remainders
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2018-10-10 18:03:03 -04:00
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---
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2020-12-16 00:37:30 -07:00
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# --description--
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2018-10-10 18:03:03 -04:00
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2021-11-23 11:06:14 -08:00
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令 $p_n$ 为第 $n$ 个素数:2, 3, 5, 7, 11, ...,并令 $r$ 为当 ${(p_n−1)}^n + {(p_n+ 1)}^n$ 除以 ${p_n}^2$ 的余数。
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2021-02-06 04:42:36 +00:00
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2021-11-23 11:06:14 -08:00
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例如,当 $n = 3, p_3 = 5$,$4^3 + 6^3 = 280 ≡ 5\\ mod\\ 25$。
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2021-02-06 04:42:36 +00:00
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2021-11-23 11:06:14 -08:00
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余数超过 $10^9$ 的 $n$ 的最小值是 7037。
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2021-02-06 04:42:36 +00:00
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2021-11-23 11:06:14 -08:00
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求余数超过 $10^{10}$ 时的 $n$ 的最小值。
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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# --hints--
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2018-10-10 18:03:03 -04:00
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2021-11-23 11:06:14 -08:00
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`primeSquareRemainders()` 应该返回 `21035`。
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2018-10-10 18:03:03 -04:00
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```js
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assert.strictEqual(primeSquareRemainders(), 21035);
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2018-10-10 18:03:03 -04:00
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```
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2021-01-13 03:31:00 +01:00
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# --seed--
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## --seed-contents--
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```js
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2021-11-23 11:06:14 -08:00
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function primeSquareRemainders() {
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2021-01-13 03:31:00 +01:00
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return true;
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}
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2021-11-23 11:06:14 -08:00
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primeSquareRemainders();
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2021-01-13 03:31:00 +01:00
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```
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2020-12-16 00:37:30 -07:00
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# --solutions--
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2020-08-13 17:24:35 +02:00
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2021-01-13 03:31:00 +01:00
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```js
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// solution required
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```
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