ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
41 lines
1.1 KiB
Markdown
41 lines
1.1 KiB
Markdown
---
|
||
id: 5900f5241000cf542c510036
|
||
title: 问题437：斐波那契原始根
|
||
challengeType: 5
|
||
videoUrl: ''
|
||
dashedName: problem-437-fibonacci-primitive-roots
|
||
---
|
||
|
||
# --description--
|
||
|
||
当我们计算8n模11为n = 0到9时，我们得到：1,8,9,6,4,10,3,2,5,7。我们看到所有可能的值从1到10出现。所以8是11的原始根。但还有更多：如果我们仔细看看，我们看到：1 + 8 = 9 8 + 9 =17≡6mod11 9 + 6 =15≡4mod11 6 + 4 = 10 4 + 10 =14≡3mod11 10 + 3 =13≡2mod11 3 + 2 = 5 2 + 5 = 7 5 + 7 =12≡1mod11。
|
||
|
||
因此，8 mod 11的幂是循环的，具有周期10，并且8n + 8n +1≡8n+ 2（mod 11）。 8被称为11的斐波那契原始根。不是每个素数都有斐波那契原始根。有一个或多个Fibonacci原始根有323个小于10000的素数，这些素数的总和是1480491.用至少一个Fibonacci原始根找到小于100,000,000的素数之和。
|
||
|
||
# --hints--
|
||
|
||
`euler437()`应该返回74204709657207。
|
||
|
||
```js
|
||
assert.strictEqual(euler437(), 74204709657207);
|
||
```
|
||
|
||
# --seed--
|
||
|
||
## --seed-contents--
|
||
|
||
```js
|
||
function euler437() {
|
||
|
||
return true;
|
||
}
|
||
|
||
euler437();
|
||
```
|
||
|
||
# --solutions--
|
||
|
||
```js
|
||
// solution required
|
||
```
|