982 B
982 B
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f48d1000cf542c50ff9f | Problem 288: An enormous factorial | 5 | 301939 | problem-288-an-enormous-factorial |
--description--
For any prime p
the number N(p,q)
is defined by N(p,q) = \sum_{n=0}^q T_n \times p^n
with T_n
generated by the following random number generator:
\begin{align}
& S_0 = 290797 \\\\
& S_{n + 1} = {S_n}^2\bmod 50\\,515\\,093 \\\\
& T_n = S_n\bmod p
\end{align}$$
Let $Nfac(p,q)$ be the factorial of $N(p,q)$.
Let $NF(p,q)$ be the number of factors $p$ in $Nfac(p,q)$.
You are given that $NF(3,10000) \bmod 3^{20} = 624\\,955\\,285$.
Find $NF(61,{10}^7)\bmod {61}^{10}$.
# --hints--
`enormousFactorial()` should return `605857431263982000`.
```js
assert.strictEqual(enormousFactorial(), 605857431263982000);
```
# --seed--
## --seed-contents--
```js
function enormousFactorial() {
return true;
}
enormousFactorial();
```
# --solutions--
```js
// solution required
```