49 lines
952 B
Markdown
49 lines
952 B
Markdown
|
---
|
||
|
|
id: 5900f4ea1000cf542c50fffc
|
||
|
|
title: 'Задача 381: Факторіал простого числа-k'
|
||
|
|
challengeType: 5
|
||
|
|
forumTopicId: 302045
|
||
|
|
dashedName: problem-381-prime-k-factorial
|
||
|
|
---
|
||
|
|
|
||
|
|
# --description--
|
||
|
|
|
||
|
|
Нехай для простого числа $p$ $S(p) = (\sum (p - k)!)\bmod (p)$ for $1 ≤ k ≤ 5$.
|
||
|
|
|
||
|
|
Наприклад, якщо $p = 7$,
|
||
|
|
|
||
|
|
$$(7 - 1)! + (7 - 2)! + (7 - 3)! + (7 - 4)! + (7 - 5)! = 6! + 5! + 4! + 3! + 2! = 720 + 120 + 24 + 6 + 2 = 872$$
|
||
|
|
|
||
|
|
Тоді $872\bmod (7) = 4$, $S(7) = 4$.
|
||
|
|
|
||
|
|
Можна довести, що $\sum S(p) = 480$ для $5 ≤ p < 100$.
|
||
|
|
|
||
|
|
Знайдіть $\sum S(p)$ для $5 ≤ p < {10}^8$.
|
||
|
|
|
||
|
|
# --hints--
|
||
|
|
|
||
|
|
`primeKFactorial()` має видати `139602943319822`.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.strictEqual(primeKFactorial(), 139602943319822);
|
||
|
|
```
|
||
|
|
|
||
|
|
# --seed--
|
||
|
|
|
||
|
|
## --seed-contents--
|
||
|
|
|
||
|
|
```js
|
||
|
|
function primeKFactorial() {
|
||
|
|
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
primeKFactorial();
|
||
|
|
```
|
||
|
|
|
||
|
|
# --solutions--
|
||
|
|
|
||
|
|
```js
|
||
|
|
// solution required
|
||
|
|
```
|