1.2 KiB
1.2 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f5351000cf542c510047 | Problem 456: Triangles containing the origin II | 5 | 302130 | problem-456-triangles-containing-the-origin-ii |
--description--
Define:
\begin{align}
& x_n = ({1248}^n\bmod 32323) - 16161 \\\\
& y_n = ({8421}^n\bmod 30103) - 15051 \\\\
& P_n = \\{(x_1, y_1), (x_2, y_2), \ldots, (x_n, y_n)\\}
\end{align}$$
For example,
$$P_8 = \\{(-14913, -6630), (-10161, 5625), (5226, 11896), (8340, -10778), (15852, -5203), (-15165, 11295), (-1427, -14495), (12407, 1060)\\}$$
Let $C(n)$ be the number of triangles whose vertices are in $P_n$ which contain the origin in the interior.
Examples:
$$\begin{align}
& C(8) = 20 \\\\
& C(600) = 8\\,950\\,634 \\\\
& C(40\\,000) = 2\\,666\\,610\\,948\\,988
\end{align}$$
Find $C(2\\,000\\,000)$.
# --hints--
`trianglesContainingOriginTwo()` should return `333333208685971500`.
```js
assert.strictEqual(trianglesContainingOriginTwo(), 333333208685971500);
```
# --seed--
## --seed-contents--
```js
function trianglesContainingOriginTwo() {
return true;
}
trianglesContainingOriginTwo();
```
# --solutions--
```js
// solution required
```